I'm thinking of shunning the transperson.
Why do you think you should shun them?
They make me nervous, the way they dress and act is a bit odd.
If they make you that uncomfortable, then you don't have to go out of your way to interact. Just make sure you're not hurting them or being rude.
I think I'll just be plain mean to them.
You're uncomfortable around people who are trans, but that's not a good excuse to shun or be mean to them. If they get to know you better, they will probably feel more at ease; that won't happen if you're mean.