I've heard tell that in Iceland, where the patronymics can be matronymics (?) - they just don't care - and then bastardy would have less of an impact, but I suppose the kids at school wouldn't be overly kind even in that kind of environment. "you've got no dad" But I haven't heard of many places like Iceland, anyway.
People like to pretend today that a lot of our western cultural mores aren't related to religion, but they are. We'd become accustomed to optimal nuclear family units and bastardy was considered more negative than when it was just a mechanism to make sure the 'right' heir got the land. In the Middle Ages, 'sport' was the term for going to the local whorehouse and having some fun, and nobles took it for granted that they could satisfy their lusts with whomever caught their eye.