It really depends on what it is.
Generally it takes a lot to offend me to the point of me showing anger or aggression, but I have very low tolerance for any kind of racist or sexist opinions and that's something I've seen a lot of. Most of the time my friends are pretty cool though, and when we fight it's usually petty stuff that isn't really worth explaining. If a complete stranger says something I find morally offensive it's easier for me to ignore that person, because I don't have to deal with them regularly.