I don't think it gets enforced much, but it's definitely there in the terms of service and help pages. You need to have written permission from the copyright holders. This is not the same as for a "regular" release, where one only needs explicit permission if it's the first recording of the piece. (After that you can record a cover under what's called a compulsory license). When recording a cover, the seller must pay mechanical royalties to the rights holder of the composition, which Bandcamp doesn't want to do (though maybe Songtradr has plans??) and we can assume artists won't bother. Because bandcamp is selling releases (rather than just streaming), mechanicals would apply.
Presumably they don't bother enforcing unless the rights holder makes a complaint.
Huh, interesting. Some quick googling suggests, this is relatively new, as a new law regarding streaming services came into effect in 2021, forcing streaming services to post, and bc didn't want the hassle. Before the law, they could require the band to have a streaming license in addition to the mechanical license.
What? Here’s a black metal cover of Hit me Baby (One more time): https://spider-god.bandcamp.com/track/baby
There are tons of covers on BC, never heard of that restriction.