It depends on your level of extremism on each.
Like, if you're a furry but you just draw animals standing on two legs because you think they're cute or fun to design, you do you. But if you own three fursuits, actively attend furry orgies, bone animals and cannot construct a coherent sentence without owo or uwu, we have a problem.
Likewise, if you're a weeb but you just casually enjoy anime and think Japanese culture is sorta neat, I'm not gonna stop you. But if you've seen every anime known to man, flick your bean to hentai every night, and are married to a body pillow, I think you need some help.
But of course, when you weigh both extremes against each other, I'd say furries are worse. Hardcore weebs are gross and pathetic people who should be avoided at all costs, but hardcore furries pose an actual threat to animals and have disgusting yiff orgies. If I were to choose the lesser of two evils here, it would be weebs, I think.