In the above conversation we don't get the full picture.
We get full picture of Sridhara Svami as seen by Gaudiya Vaishnavas in Tattva Sandarbha work of Jiva Goswami.
Text 27 of Tattva Sandarbha reads as follows:
Therefore to ascertain what is actually the highest good in life we
should focus our investigation on Srimad Bhagava-tam, carefully
reconciling its statements with what precedes and follows them. With
this aim, in this work consisting of six Sandarbhas the introductory
sentences in each anuccheda] will serve the function of sutras The
quot.ations from Srimad Bhagavatam will be the scriptural texts under
consideration. Sridhara Svami's explanation of the Bhagavatam will
serve as our primary commentary. Srila Sridhara Svami is a pefect
Vaisnava. But to entice the Advaita-vadis now a days prominent all over
Madhya-desa and other parts of the country — to become absorbed in the
glories of the Supreme Lord, he mixed some traces of their theories
into his writings. We will cite Sri Svamicarana s commentary verbatim
when its agrees with the conclusions of pure Vaisnava philosophy.
Jiva Goswami quotes Sridhara Svami's explanations in most of the anucchedas of the six sandarbhas.
Śrīdhara Svāmī is considered a Vaiṣṇava because he states in his commentaries
that the Lord’s vibhūtis, abodes, qualities and forms, as well as the bodies of his
associates are eternal and that bhakti to Bhagavān is the most attractive type of
liberation. Sometimes he writes māyāvāda ideas, but it should be understood that
its purpose is to attract the māyāvādīs to bhakti, by offering bait on a hook.
Similarly pure Vaiṣṇava philosophy accepts the non-contrary parts of Sāṅkhya.
In that way, the parts of Śrīdhara Svāmī which follow pure Vaiṣṇava ideas are
quoted.
Śrīdhara Svāmī’s writings at large are not irreproachable. Rūpa Gosvāmī was
the first Gauḍīya Vaiṣṇava to point out that Śrīdhara Svāmī’s commentary on
Bhāgavatam is not perfect.
In Laghu-vaiṣṇava-toṣaṇī, Jīva Gosvāmī attacked Śrīdhara Svāmī's explanations on
several occasions (10.3.24; 10.13.57; etc.). Still, on the whole Śrīdhara
Svāmī’s commentary on Bhāgavatam justifies Caitanya Mahāprabhu’s approval.
In many ways, he propounded the highest philosophy. For example:
tvat-kathāmṛta-pāthodhau viharanto mahā-mudaḥ | kurvanti kṛtinaḥ kecic
catur-vargaṁ tṛṇopamam ||
“Some accomplished persons who are greatly
joyful while sporting in the ocean of nectar topics about You render
the four goals of life insignificant like straw.” (Bhāvārtha-dīpikā
10.87.21) (quoted in Bhakti-rasāmṛta-sindhu
1.1.40)
A brief outline of Sridhara Svami's commentary on Bhagavatam and how it clearly is far from Shankara's nondualism and comes halfway to the metaphysical nuances of acintya-bhedabheda is described in Chaitanya Vaishnava Vedanta by Ravi M Gupta.
From a close analysis of Sridhara’s commentary on the first verse and
four main verses of the BhAgavata, Sheridan concludes that Sridhara
taught a “theistic non-dualism of sorts,” (ibid.: 57) not so different
from the BhAgavata’s own bhedAbheda standpoint (ibid.: 54). While
Sridhara employs the categories and hermeneutical tools of Advaita
Vedanta (such as the notion of essential and accidental
characteristics), he does not use them to defend Shankara’s radical
nondualism. “Sridhara . . . has moved, at least in this immediate
context, toward a non-dualism of a realistic Sankhya type, otherwise
called ‘qualified nondualism’” (ibid.: 64). This move, Sheridan
argues, brings him “halfway to the metaphysical nuances of
acintya-bhedabheda” (ibid.: 58). Perhaps the clearest evidence of
Sridhara’s shift lies in his avoidance of the concept of mAyA (the
illusory power that comprises this world) as delineated in Advaita
Vedanta. For Sridhara, mAyA does not consist of ignorance (avidyA)
that results from the superimposition (adhyAsa) of the world on
Brahman. Instead, it is the veiling, multi-faceted sakti of the
Supreme Lord, understood in terms similar to mAyA in theistic
Vaisnavism. In his commentary on the BhAgavata’s first verse, Sridhara
Svami fails to make any mention of the concepts of superimposition,
confusion (bhrama), or ignorance, despite ample opportunities to do
so. The word “nirasta-kuhakam” is glossed simply as “nirasta| kuhaka|
kapaVa| mAyAlak2aWam yasmi|s tam”—“him in whom the deceit that is
characteristic of mAyA is destroyed.” Even the line “tejo-vAri-m{dAm .
. . ,” which Jiva Gosvami himself recognizes as having potential for
an Advaita interpretation, is let off quite gently by 3rcdhara. He
interprets vinimaya as vyatyaya, the false appearance of one element
in another, like a mirage seen on a hot surface, water seen in glass,
and glass appearing like water. Although these examples are typically
Advaitic in nature, Sridhara does not take the opportunity to develop
a theory of error. This is especially significant given the fact that
Shankara’s Brahmasutra commentary begins straight away with a theory of
super-imposition. For Sridhara, the essential point here is that
despite appearances, the world finds its basis in the true reality of
Brahman, who has the power to dispel all confusion. We find another
example of Sridhara’s reticence in regard to mAyA in his commentary on
the second verse of the four-verse Bhagavata. Sheridan translates the
verse and commentary as follows: What is manifest without a basis and
is not manifest in the Self, know that to be the maya of the Self,
like an appearance, like a shadow. [Sridhara’s commentary:] This
defines maya since it was mentioned subsequently and since the linking
of maya and Self follows maya. “Without basis” means without a
substantial basis. For this reason, what is implicit in the substratum
of the Self appears real “and also does not appear,” know that to be
the maya of the Self. “Like an appearance” means the two moons etc.
which are not distinguished in perception. “Like a shadow” means the
non-recognition of something that is. The shadow is Rahu which remains
in the realm of the planets, even if it is not seen. (1994: 59–60)
As in his explanation of the BhAgavata’s first verse, Sridhara here is
satisfied to describe mAyA simply in terms of false appearances, using
examples found in the verse itself. Also as in the first verse, he is
primarily interested in the fact that the world of appearances has a
real basis in the reality of Brahman. As such, he makes no attempt to
go beyond the text of the BhAgavata to articulate a theory of
ignorance in Advaitic terms. Indeed, Sridhara was perhaps closer to
the Caitanya Vaisnava view of sakti than he was to Advaitic concepts
of mAyA. A more positive articulation of Sridhara Svami’s views on
mAyA can be found in his commentary on verse 1.7.6 of the BhAgavata.
This verse appears in a description of Vyasa’s state of trance before
he composed the PurAna, which, we have seen, is one of Jiva’s main
loci for finding the overall meaning of the BhAgavata. As such, Jcva
discusses this verse at length in the Tattva-sandarbha (from section
32 to 45). He sees in it the possibility of nondualist interpretation
and so takes the opportunity to argue against the Advaita ideas of
mAyA, ignorance (avidyA), and limitation (upAdhi). Yet Sridhara’s
commentary on this verse is remarkably simple, positive, and free of
heavyweight Advaita terminology: The learned (Vyasa) composed the
sAtvata-sa|hitA [BhAgavata PurAna] for people who do not know
bhakti-yoga for Adhoksaja, which directly removes unwanted things.
[Sridhara’s commentary] This is stated: The Lord, who possesses all
saktis, who knows everything, who has an eternally manifest, supremely
blissful form (svarupa), controls mAyA by his knowledge- sakti. The
living entity, whose true form is unmanifest, and who (instead)
possesses qualities just opposite to it, is bewildered by his (the
Lord’s) mAyA. The living entity is liberated through knowledge that is
obtained by bhakti to the Lord. That is stated by Visnusvami, “The
Lord, who is eternal, cognizant and blissful, is embraced by knowledge
(sa|vit) and the energy of bliss. The living entity is covered by his
own ignorance and is pained by masses of suffering.” So also, “He who
controls mAyA is the Lord, and he who is pained by her is the living
entity. We praise this Man-lion Lord, who continually enjoys with his
own mAyA. He possesses transcendental bliss that is manifested from
himself, and from him the world of great suffering is manifested. He
is unsullied by the fear born from the differences of the world, which
has arisen from his own glance.” And so on Here we find nearly all
the elements of the Caitanya Vaisnava concept of Bhagavan’s sakti. The
Lord is the possessor of all energies and his form is not temporary or
material, but a manifestation of his personal sakti, with which he
forever enjoys. He does, however, remain aloof from the external
energy, which comprises the world of mAyA. As a transformation of the
Lord’s sakti, mAyA is not false or illusory in itself, but only in its
effect on the hapless living entity. Its influence can be annulled by
devotion to Bhagavan. Although Sridhara Svami does not partition
Bhagavan’s sakti into three types, clearly all the elements necessary
for the development of a more systematic theory are present above.
Furthermore, the verse from Visnusvami provides the basis for a
further division of the internal energy into three parts. The only
element of the sakti concept that is missing—indeed, conspicuous by
its absence—is inconceivability (acintya). The strong emphasis on the
inconceivable nature of Bhagavan’s energies seems to be a distinctly
Caitanya Vaisnava proclivity, arising from a desire to preserve
Bhagavan’s transcendence. We may thus confirm Sheridan’s assessment of
Sridhara as “halfway to the metaphysical nuances of
acintya-bhedabheda” (1994: 58). A much more comprehensive and in-depth
study of Sridhara’s commentaries would be required to reach any broad
conclusions about his views. Whatever the outcome of such a study
might be, however, it is clear that he cannot be simplistically
aligned with, or assigned to, Advaita Vedanta.
Chaitanya's preference may just as well have been a result of appreciation for Sridhara's deep
devotion or his bhedAbheda theology not necessarily because of his Advaita affiliation, which, we have argued, is a more
accurate characterization of Sridhara's views than is pure Advaita. Also, we find Sridhara’s commentary on BhAgavata 10.43.17,
where we find the seeds of a bhakti–rasa theory centered on Krishna which is important thing in Chaitanya Vaishnavism.
From incidents of Chaitanya Mahaprabhu with Prakasananda Sarasvati and Sarvabhouma Bhattacharya, it is clear that Chaitanya Mahaprabhu didn't accept advaita. So no way he would accept Sridhara Svami's advaitic explanations whenever it was seen. And also it could be that he didn't criticize Sridhara Svami because he is considered vaishnava who wrote some advaitic explanations on purpose. Most important verse of Gaudiya Vaishnavism SB 1.3.28 is differently explained by Sridhara Svami who just says Krishna is Narayana himself. So it can't be 100% acceptance of Sridhara Svami's comments by Chaitanya Mahaprabhu. But since Sridhara Svami closely gives vaishnava conclusions most of the times, he is accepted as an authority. And Jiva Goswami follows Sridhara Svami's explanations whenever they agreement with pure Vaishnava siddhanta only. Whenever he quoted Sridhara Svami's commentary, he mentioned his name or tika ca which means Sridhara's commentary says and whenever he doesn't agree with Sridhara's advaitic interpretation, out of respect for Sridhara, Jiva does not quote him, paraphrase him, or even use language similar to his. As far as the reader is concerned, the opposing views could have come from any Advaitin.
Thus, Gaudiya Vaishnavas followed Sridhara Svami and had great reverence for him mostly because most of the his commentary is in line with pure Vaishnava philosophy, but whenever he offers an advaitic explanation, Gaudiya Vaishnavas didn't accept that.