What's the likely MIL mindset - part Ivy Tilsley, part fear, and part a fuzzy sense of it being her turn to be a matriarch?
I was raised Catholic and my guess is that many older devout Catholics aren't always very precise on details - like not knowing an Anglican baptism is considered a true baptism. (They don't think of it as essentially the same religion - the services sometimes have near-identical wording.)
Baptism doesn't need to be by a priest or vicar at all according to Catholic rules. There just needs to be water poured over the person, the words 'I baptise you in the name of the father, the son and the holy spirit' and the baptist has to intend to initiate the person into Christianity.
There's still a 'no need to ask questions beyond your paygrade' culture, especially among older people like my granny - which is why they mightn't know all the details. She was worried when my kid was christened late in case they died suddenly and didn't get to go to heaven. But more I think because christening older children is seen as less respectable!
I said my baby wasn't sinful and wouldn't go to Limbo if they died, which I was planning on avoiding if possible.
Some more traditionalist women becoming grandparents now probably expected to get their way over younger family members for things like christenings. Because that's how they were treated back in the day. But we're not putting up with it, quite rightly. They committed to a whole value system which is now fizzling out.
The saints names thing is funny and again I think there are some old ideas out there, which some traditionalist or awkward priests would have encouraged. Some older posters on Mumsnet are similarly strict about not naming babies Harry instead of Henry etc because they feel it's breaking the rules of naming, though not for religious reasons.
Cherie Blair's christening name was Teresa, apparently. She's quite religious, but she obviously likes her real non-saint name.
Apparently the guidance to have a saint's name was a cultural thing to encourage attachment to Catholic identity and sense of a relationship with your own saint. In the old days the saint's name rule was probably a way of a grumpy priest telling young parents not to think they were too special by choosing funky modern names. I'd imagine contemporary priests would draw a line at a Pagan or Styx but would probably be fine with a Rainbow or Aria.
I've just checked if there's an official register of saints (!) There's something called the Martyrologium Romanum with over 7000 names on it, at https://archive.org/details/MartRom2004
Brilliantly, St Patrick isn't an official saint, but I can't imagine they would ever say no to a baby Patrick. Catholic rules!