Maybe Flanagan was just having fun with a creative take on the vampire theme. It's not the virgin birth or the resurrection that's so relevant here, though, as a connection between Catholicism and vampirism, but the Eucharist ceremony.

But those three long monologues on the nature of death seem to me the central concerns, and the contrast they set up is between mature (Eastern or pantheistic) religions and dubious, immature ones (e.g. Catholicism which might as well be just a vampire fantasy or misunderstanding, for all we can tell with the available evidence).

The show's implications are pretty skeptical, as far as I can see.

I'm also keeping in mind Flanagan's other work which pits skepticism against the supernatural, and in which the latter wins out. But Midnight Mass seems a more personal statement since Flanagan wasn't adapting other stories but creating a new one here.