tell her this, there is really no proper definition for normal, since everyone is unique in their own way, no one is the same, everyone is different. Tell her that your interests are different from your sisters because you and her are different people. Tell her some more about the fandom, prove that fursuiting is fun, and that it's not for homosexuals (how did she even conclude to that?) Point out that the fandom is about creativity and your mom not letting you do things in the fandom, tell her that she's in your way of being creative to your own extent.
Also, tell her that since your in this fandom, you will not end up like those who are addicted to drugs or something like that, since being creative like this wouldn't end up with drugs in any connection. Also, tell her that when doing fursuiting, it improves your people skills, acting, stuff like that.