I would walk up to her. I would be polite, and say something like “I couldn’t help but overhear your conversation about marriage and the Catholic Church,” and then I would wait for HER to say something. She’ll either say, “MYOB” (or something like that, hopefully politely, making it clear that she has no interest in hearing from strangers), or in all likelihood, since this sounds like the kind of restaurant where people chat, she’ll say, “Yes, are you Catholic?”
As I said, this sounds like the kind of restaurant where people are looking for friendly people. Diners are often like this–a counter where people sit who want to chat, and tables fairly close to each other so they can chat.
I love these kinds of restaurants, and my brother does, too–when he goes to one of our favorite places, he deliberately sits near the front because he says hi to almost everyone who walks by, and often, they will sit down with him for a while to chat and drink coffee, and sometimes, they’ll sit with him for the whole meal. I’ve done the same–I’ll go in, and say “Hi,” and it turns into a friendly chat, and we end up eating together! (I do this with woman, not men, since I’m a gal.)
I live in Northern Illinois. My daughter lives in NYC, and she does the same thing with a few coffee shops and pizza places–chats with the other diners.
Often these restaurants have names like “Sit and Sip” or “Sit-A-While” that kind of imply this is a place to just sit and enjoy the company of other diners. LOVE these places!
There are other restaurants where this would NOT be a good idea, and where people come strictly to dine and be with their partner or friends, and are not interested in chatting with people they don’t know. You know what kind of restaurant you were in.
But I still recommend at least opening the door for this woman to talk to you, and if she doesn’t seem interested in going through the door, then don’t push it. Just say, “I’m sure it’ll work out for you. Have a good day,” and walk away.
BTW, I hate it when I go into a restaurant or coffee shop, and everyone is sitting there with heads down, engrossed in their stupid phone. IMO, they shouldn’t be in a diner where people have always enjoyed chatting and making “dining friends.”