It might be worth you or your friend to introspect on why that behaviour makes you feel the way it does.

I don't really think the onus is on us.

A lot of multiplayer games have become very toxic, tons of cheaters (okay I don't actually believe this but it's a very common perception; I mostly blame smurfing and bad MMR systems), rude people, etc. It can transform a fun evening into dealing with "TotallyNotANazi" and his buddy "TotallyNotARapist" calling you names, t-bagging your bodies, screaming obscenities, and in some cases, likely using cheats, to make nearly impossible shots.

The other fun one (that's not quite as bad) is when you've been having a clean match with someone, you're clearly winning, you haven't been rude to them at all, then they get one kill on you and it's time to run up a t-bag and get on the microphones or text chat about how you're shit at the game.

The better strategy would be to improve moderation and kick these people out of the games. However, multiplayer gaming has moved from server owners that can ban bad actors to "someone at the studio has to do it" (and frankly, the studios are not holding trolls, jerks, and cheaters accountable).

Games like CSGO have added options like hiding usernames, hiding profile pictures, etc. I just see this as part of cleaning up the rest of it. If you're not going to moderate the multiplayer game to get rid of the most unruly jerks in your community, there should be options for "I don't want to see their nonsense."

Personally, I play shooters to relax, not to be some jerk-wad's punching bag. I don't really mind it if the enemy team is joking around and just being playful about it, but some people are clearly out to just put people down and I don't think they should be the priority; I think they actively keep some spaces of gaming as this cringe elitist thing a lot of people just don't want to interact with.