As far as i know most MMOs don't run heavy anti cheat stuff as they are built to not trust the clients so i suspect a lot will work fine.

Some i know work perfectly fine are:

Guild wars 2, both through lutris and proton. Back when i originally swapped to linux i had some issues getting the commonly used dps meter (arcdps) to work with proton. It requires some optional features to be enabled to allow direct x overlay windows etc. Worked first try through lutris though and ive been playing the game on and off for the past year through that without issues.

The Elder Scrolls Online, works perfectly fine through proton. You can even get the standard addon manager (minion) working through standard wine and just point it at the right folder for addons to work. A few that require running programs to update stuff will be fiddly though. (Like tamriel trade centre)

Final fantasy XIV has an unofficial launcher (XIVlauncher) you can snag up on the flathub that makes installing and running the game easy. I have not played the steam version, but i imagine it works as well.

Warframe works fine through steam, but its barely an MMO.

Second life works fine with the common viewer, firestorm, having a native linux version.

!2007scape@lemmy.world. RuneLite works fantastically.

RuneLite is linux native though. If you want something specifically through Wine, others have said Guild Wars 2 and FFXIV, but I've also heard good stuff about STAR WARS: The Old Republic. And if you're okay with something a little more obscure/"out there", Shakes and Fidget has great reviews (it's a satire on MMORPGs).

FF14 is fantastic through XIVLauncher. ESO works out of the box, and so does Guildwars 2. There's plenty to choose from!

I’ve been reasonably happy with how Final Fantasy XIV runs on Linux. XIVLauncher makes setup easy and I the game is fantastic

It's not exactly an MMORPG but rather an MMOFPS but Planetside 2 works very well.

As a rule of thumb if it's available on Steam and you play it through Steam it will probably work. That said always good to check ProtonDB

I've played a bit of CoH Homecoming and Guild Wars 2 via Lutris, no issues. I know neither of those are particularly new games, but they run fine.

Not sure if it's your cup of tea, but Old School Runescape runs perfectly on Linux. I use the Runelite client too for better graphics, in game quest guides, etc and it runs great.

The newer Runescape also runs very well too.

Veloren https://veloren.net/

eso and fo76 work pretty good. pokemmo is good too but i have been banned too many times (because i made it a game to play factorio with opencv instead of pokemon lmao)

I played for a lot of time Elder Scrolls Online on linux without any problems (except some addons) but in generally it works really well, without performance problems or something else. I used the official launcher with lutris and had a lot of good time playing it.

I've had success running EVE Online on Linux before. There was an unofficial Linux client from a staff but I'm not too sure the current state of it since I haven't played it for awhile now. It has a Gold rating on ProtonDB.

Final Fantasy XIV works great.

New World plays alright, in the bit I've played since switching. Generally a good game too ☺️

Digging New World and Albion Online at the moment. All those others are great, too. ESO can get tricky to install addons is my only comment there.

Dota 2?