A genre is a volume in song space.
More seriously, there’s no reason you can’t assign more than one genre to a song, or say that “it’s a mix of A and B”. You can extend the concept to albums and artists just as easily.
I’m not familiar with R.E.M., but on rateyourmusic.com they’re marked as alternative rock, jangle pop, pop rock, indie rock, neo-psychedelia, and folk rock. “Don’t go back to Rockville” is marked as Jangle pop, and the “Reckoning” album overall is mostly Jangle pop with some influences from post-punk and Paisley Underground.
You may not agree with these categorizations, but it’s a crowd-sourced website so you can go vote for different genres. You may also disagree with the existence of all of these genres, some of which I’ve never heard of myself (but as I said, I haven’t listened much to R.E.M. in general), but my point is more that if you’re familiar with them then you kind of know what to expect from the song.
I’d never heard “don’t go back to rockville”, but just from these genres you named to make your point, I already knew what it would approximately sound like. And indeed listening to it confirmed that.