Why did Sri Adi Shankaracharya said like this in Sarva Vedanta Siddhanta Sangrah सर्वस्यानित्यत्वे सावयवत्वेन सर्वतः सिद्धे । वैकुण्ठादिषु नित्यत्वमतिर्भ्रम एव मूढबुद्धीनाम् ॥
When it is established that everything made of parts is ephemeral, those of lowly intellect are deluded thinking that vaikuṇṭha, etc. are eternal.
Pls answer according to Vaishnava perspective
Firstly, Not only Adi Shankara but Sri Madhusudana Sraswati too, in the Advaita Siddhi, refuting the claims of the Dvaitin, concludes:
[Pariccheda 2, p.745 of the Edition published by MM Ananthakrishna Shastry]:
//etena bhagavallokaaderapi nityatvam apAstam. Na cha ‘ato hi vaiShNavA lokAH nityAste cetanAtmakaaH. matprasAdAt parAm shAntim sthAnam prApsyasi shAshvatam’ ityAdyAgamavirodhaH, tasya avaAntarapralayasthatvaparatvAt. TasmAt nirguNam nirAkAram brahma iti siddham. Iti advaita siddhau brahmaNo nirAkAratva siddhiH//
[Thus (in view of the foregoing arguments), the ‘eternality’ of divine/lordly/worlds too stands negated. One aught not to raise an objection that the following scriptural passage is contradicted by the above conclusion: ‘Therefore indeed the VaishNava loka-s are eternal and are sentient in nature. By My grace you shall attain the state of great and eternal peace.’ The ‘eternality’ stated in this passage has its purport in the ‘avAntara pralaya’, intermediary dissolution. Thus stands established that Brahman has no form in the work called ‘Advaita siddhi’.]
Secondly, Adi Shankara was a nondualist who ascribed nityatva (eternality) to nothing other than Nirguna brahman while all Vaishnava philosophers are dualistic who believe in the eternality of the Saguna form and Loka of God and see the concept of absolute unity (in the Advaita sense) itself as false. So there is no point in attempting to 'reconcile' Adi Shankara's statements with the philosophy of a Rival school.
As far as the Vaishnavite stance on Adi Shankara is concerned, Vaishnavas simply believe Adi Shankara's philosophy itself to be false on the basis of Padma Purana, Uttara khanda chapter 236.
The doctrine of Māya (illusion) is a wicked doctrine and said to be pseudo-Buddhist. I myself, of the form of a brāhmaṇa, proclaimed it in Kali (age). 8-12. It shows the meaninglessness of the words of the holy texts and is condemned in the world. In this (doctrine) only the giving up of one’s own duties is expounded. And that is said to be religiousness by those who have fallen from all duties. I have propounded the identity of the Highest Lord and the (individual) soul. I stated this Brahman’s nature to be qualityless. O goddess, I myself have conceived, for the destruction of the worlds, and for deluding the world in this Kali age, the great doctrine resembling the purport of the Vedas, (but) non-Vedic due to the principle of Māya (illusion) (present in it).
So from the above, the only "explanation" of it as per a Vaishnava perspective would be that he said so to cause delusion
Of course, the validity of the above Purana statement itself can be critiqued on several grounds, but I won't be going into them, since that is not the subject of the question
