There is tons of evidence in favor of them being a furry, but not 100% evidence. If James didn't like the meme, they wouldn't keep milking it. Personally, I am 80% sure that they are.
And from your comment, I can see that you don't quite know what a furry is actually. I you'd be willing to learn more, I recommend Anthony Padilla's video where they interview a few furries. This might help you get a better understanding of the community. The video is literally 11 minutes, so its not long.
And they're sweating because this is a comic that they made awhile ago that has been made customizable. I simply added the "James is a furr-" as a joke. Again, they wouldn't fuel the meme as much as the do if they didn't like it.