I am the furry. In the past 5 years I've played a
>Lizardfolk (DnD)
>A wolf guy (a premade Dragonbane character)
>Mon Calamari (the Admiral Akbar race)
>A half-orc (AD&D)
I doubt it really makes a difference to anyone else playing, and I keep getting invited to new games. What am I going to do, roll to knot them? Spend 15 minutes describing the texture of my own scales?
I bet half of you fantasize about elf sex or play waifu characters, so who are you to judge me?

If anything you should always be more worried about what the GM is into anyway, since their ability to change the world and impact your time playing is several times higher.