I completely agree with that verse and the question that you've posed, and there are a few things I'd like to add/clarify:
A furry is simply a fan of anthromorphic animal characters, and its not all about dressing up (most furries can't afford a fursuit anyway).
I also want to address a common misconception:
Being a furry is not inherently sexual in any way.
Having sex in a fursuit would be pretty difficult anyway. From what I have seen it's just a fun hobby, just like dressing up for comic con or liking model train sets. In fact, I would argue that being a furry could easily be used as a way to glorify God, in the sense that you could share God's word with other furries. I've seen several Christian furries who do this, and when they put on a fursuit its not for sex or perverted things, just fun.
I myself was skeptical of the Furry Fandom, spending monthes quietly lurking around various furry communities and researching about the fandom, before I finally reached a conclusion and decided to join.
Can a Christian be a furry?
Yes, definitely.
To say otherwise would basically mean that ANY hobby WHATSOEVER is sinful, because you could essentially use it for perverted things. Anything God gives us to make us happy can be used in a perverted way. Do you enjoy Mario games? Well, there is a lot of Mario themed porn. God gives a man a rock to make tools out of, but then the man might instead use it to kill his brother.
In summary: Just because something CAN be used for sin does not make it inherently sinful.