Probably many of the Irish language songs I'm thinking are from before the 19th century but I'm thinking of the subject matter rather than trying to date the material. There are some songs which tell of a priest's love for a woman or a woman's love for a priest, for instance An Sagairtín and An Caiseadeach Bán / Thug Mé Ruide

Looking to see where the lyrics are on Mudcat, I came across a thread, songs in Irish about Priests https://mudcat.org/thread.cfm?threadid=66057#1093190

Thug Mé Ruide and An Caiseadeach Bán https://mudcat.org/thread.cfm?threadid=66390

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The Galway Races is a 19th century song. It doesn't say much about religion but has a great final verse:

There was half a million people there of all denominations
The Catholic, the Protestant, the Jew and Presbyterian.
There was yet no animosity, no matter what persuasion
But fáilte and hospitality inducing fresh acquaintance.

https://mudcat.org/thread.cfm?threadid=3716#19319