What game do you recommend someone who likes the mechanics but not the setting of Baldur's Gate 3?

If you liked these, you can check out the other games by Larian - Divinity: Original Sin (1 and 2). There's also Star Wars: Knights of the old Republic (very old game though). Also, Never winter nights 2. I'm sure there's a bunch more.

Divinity: Original Sin 2? I suppose it looks a little bit gorey too, but nowhere near that high definition. Definitely no squirmers...

Pillars of Eternity 1&2? (only 2 has turn based combat) They're free* on gamepass if you got it. Don't play the console versions of 2.

Divinity: Original Sin 2! It's by the same devs and it's absolutely incredible. Different classes and spells and stuff, but you'll pick it all up very fast, and I actually think character building in Divinity is a lot more fun than D&D, because there's a lot more flexibility about how you choose powers and abilities.

If you'd prefer to stick with something based on the D&D mechanics, Owlcats games are excellent (it's Pathfinder, but Pathfinder is just a lightly modified D&D 3.5)

I recommend one of my favourite CRPGs of all time: Neverwinter Nights - for the modern hassle-free experience, get the Enhanced Edition. The first single-player campaign is pretty meh by Bioware standards, but the expansion packs (included in the NWNEE) are pretty great. Heard a lot of good about the premium modules (a few of the original premium modules come with NWNEE, the rest are available as DLC).

The official campaigns are set in Forgotten Realms, the same D&D setting as BG3, but you really don't need to worry about diving headlong into horrors. More fantasy vibes and less visceral stuff. (the second expansion pack is a bit more in the direction of subterranean spooks, but not, like, excessively so.)

However, the real big strength of NWN was not the campaigns. It was deliberately designed for player-created adventure modules created with the included Aurora Toolset. There's loads of them and some of them had really great production values and writing. They're currently hosted at Neverwinter Vault and NWNEE also has a custom content browser (though the latter doesn't have much stuff). Custom modules also have a whole bunch of genres and settings, as expected.

Oh and it's a game from 2002 so it runs on any ol' potato. (Well the EE needs a vaguely modernish machine, but not anything unreasonable.)

Planescape: torment. Just do it

Fallout 1, 2 and Tactics.

Shadowrun Returns.

Warhammer 40,000: Rogue Trader.

XCOM.

This does only assume by setting you mean "fantasy." If you just mean Forgotten Realms, there are tons of fantasy turn based tactical RPGs. Owlcat has a bunch of good shit like Kingmaker and Wrath of the Righteous.

Maybe Solasta: Crown of the Magister? I haven't played it yet, but I have read that it does D&D mechanics pretty well.

(My other ideas have already been mentioned by others.)

Planescape Torment, the shadow run series of games as well.

There are Pathfinder games by Owlcat, that is a round about earlier version of DnD (based on DnD 3.5? But its system is slightly different). I'd say they're as good of a successor to Baldur's Gate before BG3 that you'll get. The settings are similarish but not exactly the same as Baldur's Gate. I sort of lump in most DnD settings together though, Kingmaker is transforming a land and becoming a ruler, Path (Wrath*) of the Righteous I haven't played as much to recall the overall setting but definitely has a more other planes feel to it than Kingmaker does.

*Edited for title correction, thank you commenter that noted it.

Is any form of violence or blood a no-no? If you can accept some, Larian (bg3's developper) was already well known for the Divinity series. Many even say that BG3 is kind of Divinity:Original Sin 3 with a DnD license. You'll still be killing some people though. Otherwise, I suggest searching for Turn-Based games which BG3 is. You might like Battletech which is a mech warrior themed game or the X-Com series where there's an alien invasion.

And also, you might have been mislead by the videos. Yes the brain parasite is important but you're really only directly dealing with mind flayers (the tentacle clad monsters) in the very beginning and very end. The rest is just a classic fantasy setting.

I think Fallout 1 & 2 have a lot of parallels. The first two fallouts are a lot more like ttrpgs, it was when Bethesda bought them they became FPS rpgs.

Oviously older, but they hold up pretty well and certainly a different setting.

BG3 follows the formula of Dragon Age: Origins very closely.

Are you playing with a controller or M/KB?

There are plenty of other CRPGs (good search term) that are fine with a mouse/keyboard. Larian kind of stands alone in terms of how well they handle with a controller though. Divinity Original Sin 2 is still dark, but not as in your face about it.

Other terms that have similar battles (but generally more closed maps) are tactical RPGs, strategy RPGs, turn based tactics or turn based strategy. I can't break down the lines between any of those sub-genres, but they're all kind of in the neighborhood. A lot of them are also dark, though.

Not sure if there's any less gore/horror in them, but the Wasteland games are also hugely popular post-apocalyptic RPGs with turn-based combat.

Divinity Original Sin 2

Mass Effect

Marvel's Midnight Suns has similar top notch graphics, and somewhat similar mechanics, but with deck building added. I don't remember if there's a class system.

If you like the d&d mechanics, check out Solasta, which I like a million times better than BG3. The graphics aren't as good, but it's also not as gore/horror focused.

Mmmmaybe XCOM 2?

Ok I actually haven't played BG3 yet lol, but I'm gonna suggest Freedom Force. It's a superhero RPG with some cool character building. The game is on Steam and GOG but I see some people saying the GOG version works better out of the box for modern Windows.

It doesn't have dialog trees though just combat. But it's not violent, you said you didn't like the violence. And it takes very little storage space.

Fallout 1/2