Report it depending on what the insults are. Look to a moderator or an administrator for help. Don't take matters into your own hands. Don't reply to them. Consider the conversation over between you and that member.
It depends tbh, if it's in a forum or social media.
In social media i couldn't care less. If it's a forum then i might try to reply and i would show some willingness to talk the situation before doing what @Terminated suggested.. if the case goes worse then i will proceed to ignore all of that member's posts.
It's simple, here's an example, in my highschool we were debating over pro-feminism and after my turn this girl said, "ok let me add this to the list of things I don't give a fuck about". I replied with "neither did God when he made you". She was pale, everybody was laughing.
How to react to insults against your peers? Counter insult.
I used to receive hateful e-mails in the early 2000's from people that didn't like one of my sites. lol I even got actual death threats. I ignored them. lol
As for forums, it's only happened a couple times, and I let the mods take care of it. One time though, I did make a reply, then never returned to that site. Nothing insulting, I just had to get some stuff off my chest.