The major ones are already listed, so I mention only a few lesser known ones:

• https://trigger-rally.sourceforge.io/
• https://sourceforge.net/projects/extremetuxracer/
• https://juzzlin.github.io/DustRacing2D/

There's a few, mostly closer to simulation than tux kart tho. A few that I'm fairly sure are under active development:

Stunt Rally.

VDrift.

Speed Dreams. Can't easily find the github for this one.

Sonic Roboblast 2 Kart and its successor Dr. Robotnik's Ring Racers are open source, and pretty fun! The exact degree to which they're free-as-in-libre depends somewhat on Sega's policy of turning a blind eye to fan games, so although GPL-2.0 permits commercial use I wouldn't recommend testing it.

There is a lively modding scene (or there was for SRB2K last time I was playing it; I haven't played RR yet). Ring Racers has single-player content if that's what you're looking for, I hear it's quite challenging.

I suppose Rigs of Rods fits the bill, although I never played it.

The others I'm aware of (that still seem to get updates) are Stunt Rally and TORCS.

Media files are proprietary and it's under the zlib license if that disqualifies anything, but for a somewhat decent experience, there is H-Craft Championship. Not the greatest of games considering it's a game that originally released in 2007 as a commercial game available for Linux (don't know about other platforms outside of the 2015 open source(?) release) by some seemingly random independent studio (Irrgheist), but fun enough I guess.

I put together this giant list of free Linux games a while back, which also catalogs if they are open-source and what license they are released under. From the Racing section, I would second @ryven@lemmy.dbzer0.com's suggestion for Sonic Robo Blast 2 Kart :)