Also, is there any great way to tell my friend that I am not a furry while I was caught playing a furry galgame in front of him?

If it has some special mechanics or so, you can try to shift focus on that.

But why this noticeable Furry-aversion in the first place? If they treat you worse because of just guessing you are a Furry, they are not nice people to begin with. Honestly same goes for thinking less of someone for being openly part of the Furry community.