I can recommend Selaco. It's built on GZDoom and one of the best shooters I've played in the last years.

https://store.steampowered.com/app/1592280/Selaco/

Xonotic, an open-source arena shooter

Team Fortress 2

Deep Rock Galactic. Rock and stone, miner!

I have tried all these on Linux through proton.

Dusk - the OG boomer shooter revival game, should be the first game to try to see if you like these kinds of fps.

Amid evil - beautiful looking FPS instead of firing guns you fire unique magical weapons.

Ultrakill - extremely difficult movement shooter with a very interesting setting and lore. Its still not fully complete theres like a final layer thats still cooking but what's there is worth experiencing.

Selaco - FEAR inspired FPS built in GZDoom somehow. Tight movement, great gunplay, interesting enemy difficulty progression, superior AI that will flank your ass and hammer you with what feels like tactical actions, great interactive environments.

Turbo ultrakill- one of the most fun and bombastic FPS ive ever played. Play as a merc who gets turned into a living chainsaw as you ruin the plans of wannabe trancendent techno gods and run away super AI one bullet at a time

Cultic - plays heavy into blood and residents evil 4 inspirations to deliver a very mood atmospheric FPS with the best goddamn dynamite throwing mechanics since OG Blood itself. The single dev is really passionate and is constantly sharing updates to episode 2.

Ion Fury + ion fury aftershock A love letter to the best parts of build engine games of the 90s. Its incredibly well made build engine game with huge sprawling enviroments and too many secrets. The pistol with auto-lockon is hands down the best pistol Ive every used in any game. Aftershock DLC is even better than the base game.

Zortch - another passion project made by one person with an in-house engine coded just for the game. The enemy AI moves around a lot and the cartoony graphics and plot make it more of a light hearted title to have fun with like a game you would find on the N64. Its only 5$ and easily worth it.

Open Arena

Try Ravenfield. It doesn't get anymore casual than that. The most fun you can have with a battlefield like game without any of the BS.

Dusk, definitively try that

Serious Sam

Roboquest

Any Boomer Shooters like Dusk, ULTRAKILL, Zortch, Cultic, ROBOQUEST, etc.

Anger Foot natively supports Linux, and I'd consider the gameplay loop to be pretty casual.

To sum it up, you kick down doors and shoot your way through rooms while having hardcore EDM blasted at you. It has a Hotline Miami vibe to it, but is FPS.

Trailer with gameplay footage

Combat Master. Like CoD but simpler, no waiting, you start the game and end up playing in less than 2 mins, loading included.

Tf2 is the vwst war themed hat simulator out there

Iron Maiden

Was just playing Gunslinger:Juarez , it is well produced, runs perfectly and is pretty fun.

Half Life 2.

Ravenfield is a great choice if you want a Battlefield like experience, but offline against bots.

Red Eclipse, although I'm not sure how large the player base is

Halo Infinite.. still works on Linux.

Battlebit Remastered is pretty fun but I have limited experience in that one.

Ravenfield for cartoony/low poly acradey fun

Operation Harsh Doorstop for something more like Project Reality

Totally Accurate Battlegrounds is really fun and silly. Doom Eternal is also cool.

Lots of good ones here, but I'll add one I haven't seen, cube 2: sauerbraten

If Sunset Overdrive by Insomniac is too casual and platformy, there are oldschool Quake games just remastered that can make anyone's blood boil with a pretty okay difficulty scaling.

Many games have launchers which can be skipped by entering a command to the launch properties in Steam. Check the games info page in ProtonDB

What is a casual shooter? As opposed to... a serious shooter?

Alien Arena, Urban Terror, Xonotic

Mullet Madjack.