The amp can't reproduce the bass fundamentals - there's no risk of damage from something that isn't there.
Unless the amp has some specific type of filter involved that removes the lows, I don't believe that's how that works. To the contrary, to the best of my knowledge, frequently since guitars don't really have much of that low end content, I seem to recall that guitar amps may actually be less likely to have those sorts of protections in place.
The only thing that can get you in trouble is plugging a bass amp into a guitar cab and that's regardless of what the source instrument is.
As a PSA for anybody looking to follow this advice, this is also not true for the same reason I note above unless I'm mistaken (happy to be corrected).
Guitar amps are used with bass somewhat frequently, especially in recording situations. They can sound good and can reproduce lows similar to a bass amp. The key is to not try and push the cab past its limits - simple as that, and that means different things for different cabs regardless of whether they're meant for guitar or bass.