I'm very close friends with my ex-husband, but I think it would be tasteless for either of us to attend the other's wedding. So, I think it would be equally tasteless of someone I married to have an ex-spouse at the wedding. I don't think it even has to particularly be a matter of who's "bothered" by it. I think people could easily be in situations where nobody (including the new, spouse) would really care. It's just that it's tasteless - no matter how big, small, informal, or formal the second wedding is.
There are other ways to share in a friend's (ex-spouse's) happiness and new life if people feel it's important. (Small get-togethers, family get-togethers, maybe even dinner with the three/four "key characters", particularly if the new couple wants to set a foundation for friendship because of shared children; a wedding gift, etc. etc.)
It's just that I think there ought to be some boundaries and good taste when it comes to the actual wedding. If I imagine my ex-husband getting married again (considering we're close friends and have three kids), I can picture my taking the couple out to a nice dinner (with or without our grown children) shortly around the the time of wedding, and giving them a gift. I think that would be a nice way for me to wish them well, show my happiness for them, and share their happiness - without letting a big cloud of the past be anywhere near their happy occasion.