De réir GGnaBC
4.18 Ní shéimhítear

ar lorg Féile (ginideach), Naomh, San, Dé (= lá), chun:
Lá Fhéile Pádraig;Oíche na Féile Bríde; litreacha Naomh Pól; dúnmharú San Tomás; oíche Dé Máirt; chun bean an tí; chun Pádraig

An féidir libh a insint dom cén fáth a (? go) bhfuil Tuairim is 13,500 torthaí Ó Google nuair a chuirim "scoil san phroinsias" isteach ann.
Níl ach 7 torthaí ann le “ scoil san Proinsias” gan a séimhiú.

Go raibh maith agaibh arís.

Traditionally, AFIK, lenition is suppressed on Saint' names (maybe it was felt to render the name more of a common noun). I suppose a lot of people without traditional Irish are not aware of this

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__̴ı̴̴̡̡̡ ̡͌l̡̡̡ ̡͌l̡*̡̡ ̴̡ı̴̴̡ ̡̡͡|̲̲̲͡͡͡ ̲▫̲͡ ̲̲̲͡͡π̲̲͡͡ ̲̲͡▫̲̲͡͡ ̲|̡̡̡ ̡ ̴̡ı̴̡̡ ̡͌l̡̡̡̡.___

I wouldn't trust Google for such a thing... If you search for "Gaelige" or loads of other Irish words with a mistake in them, you'll also find loads of occurrences. That only shows that most of the people who write in Irish on the web make mistakes...

I rather trust Tobar na Gaedhilge - I searched for "San + saint's name" in it, but it looks like it's not that common in native Irish since all the results were either in Spanish phrases (San Francisco etc) or with "san" as an emphatic suffix (dó-san, a leabhar-san etc) which is a different word...
When there's no other possibility to verify, I tend to trust GGBC rather than google

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne