Hey Ruchi,
I’ve noticed in the religious community that I’m getting invited to weddings and bar mitzvahs that are out of town and that I would SO OBVIOUSLY not attend because we are not that close to the people, etc. So and so’s daughter is getting married in NY. So and so’s son who used to live here is having a bar mitzvah in Chicago, etc. Do I then I have to send a check or a donation? I sort of feel like… just because one person has the (in my opinion) chutzpah (too strong, I know, but not sure right word) to invite me when it would be pretty extraordinarily to leave town for an acquaintance’s relative’s event, why do I then have to be in the position to send a gift. It happens a handful of times a year. If it were an event in town, it wouldn’t bug me as much. Though even that can feel a little unnecessary based on the VERY CASUAL level of friendship I”m talking about. Friendship is not even the right word… just people I know.
I did not edit this so sorry for typos and general nasty tone. I just opened another invite so was feeling it in the moment.
I have definitely noticed this difference between the religious and secular communities.  Orthodox folks, for some reason (like their guest lists aren’t big enough as it is) invite everyone and their mother to their simchas. It’s just a way of being inclusive.  Gifts are not expected when people don’t attend, unless you’re close – even then it’s in poor taste to “expect” a gift, but you know what I mean.  They’d probably be shocked if you sent one and would then say, “Oh my gosh!  Can you believe they sent a gift!  That was so unexpected and sweet of them.”
But I do always send back the reply card and say thanks so much for including me, and I’m so sorry we cannot participate in person, and end with a blessing (which they’ll appreciate just as a gift) like “May you build a beautiful Jewish home of which everyone can be proud!”
Or to a bar mitzvah boy or bat mitzvah girl, “May you grow up to be a wonderful member of your family and community, and bring much nachas to all!”
Hope that helps,