As per manusmṛti book X, such a marriage will affect fitness for the sacraments :
anāryāyāṃ samutpanno brāhmaṇāt tu yadṛcchayā | brāhmaṇyāmapyanāryāt tu
śreyastvaṃ kveti ced bhavet || 66 ||
If a child is somehow born to a brāhmaṇā from a non-ārya woman, and
another is born to a non-ārya from a brāhmaṇā woman, with which of
these would the ‘superiority’ lie?—(66)
jāto nāryāmanāryāyāmāryādāryo bhaved guṇaiḥ |
jāto'pyanāryādāryāyāmanārya iti niścayaḥ || 67 ||
The decision is that—‘one born to an ārya from a non-ārya woman may
be an ārya in quality; but one born to a non-ārya even from an
ārya woman is always non-ārya’—(67)
tāvubhāvapyasaṃskāryāviti dharmo vyavasthitaḥ | vaiguṇyāj janmanaḥ
pūrva uttaraḥ pratilomataḥ || 68 ||
The settled law is that both these are unfit for the
sacraments:—the former on account of the defect in his birth and the
latter by reason of his being horn ‘in the inverse order.’—(68)
subījaṃ caiva sukṣetre jātaṃ sampadyate yathā | tathā'ryāj jāta
āryāyāṃ sarvaṃ saṃskāramarhati || 69 ||
Just as good seed grown in a good soil turns out well, so is the child
born to an ārya from an ārya woman worthy of all sacraments.—(69)
bījameke praśaṃsanti kṣetramanye manīṣiṇaḥ | bījakṣetre tathaivānye
tatraiyaṃ tu vyavasthitiḥ || 70 ||
Some wise men extol the seed, while others the soil; while yet others
extol both the seed and the soil. The decision on this point is as
follows.—(70)
akṣetre bījamutsṛṣṭamantaraiva vinaśyati | abījakamapi kṣetraṃ kevalaṃ
sthaṇḍilaṃ bhavet || 71 ||
The seed sown on barren soil perishes prematurely; and soil without
the seed would be a mere barren plot.—(71)
yasmād bījaprabhāveṇa tiryagjā ṛṣayo'bhavan | pūjitāśca praśastāśca
tasmād bījaṃ praśasyate || 72 ||
Because through the power of the seed, those born of animals became
sages, honoured and extolled, therefore it is the seed that is more
important.—(72)
anāryamāryakarmāṇamāryaṃ cānāryakarmiṇam | sampradhāryābravīd dhātā na
samau nāsamāviti || 73 ||
Having examined the non-ārya behaving like an ārya and the ārya
behaving like the non-ārya, the creator declared ‘that these are
neither equal nor unequal.’—(73)
For the first part "ārya in quality..." of X.67, IX.23 & IX.24 could be the example cases :
akṣamālā vasiṣṭhena saṃyuktā'dhamayonijā | śāraṅgī mandapālena
jagāmābhyarhaṇīyatām || 23 ||
The low-born akṣamālā united with vasiṣṭha, and the śāraṅgī united
with mandapāla, became worthy of worship.—(23)
etāścānyāśca loke'sminnapakṛṣṭaprasūtayaḥ | utkarṣaṃ yoṣitaḥ prāptāḥ
svaiḥ svairbhartṛguṇaiḥ śubhaiḥ || 24 ||
These as well as other women, of low birth, have attained eminence in
the world, through the good qualities of their respective
husbands.—(24).