Hearts of Oak doesn't have any racists or skinheads or racist skinheads in our group. We're pretty good at moderating who joins and who doesn't. As far as hats go - yeah, our hats are awesome. We've got some really nice ones this year too.
Concerning your group - Do you. Don't worry about what people have to say. We (the forum) have had a lot of groups form here and we do our best to help them grow. Just be cool about it. Bashing other groups about nonsense will only polarize people.
Some constructive criticism - 'The Natives' has a very negative connotation associated with it. There's a reason it didn't pick up prior to Third Rail naming themselves. "The Natives" were historically considered Know-Nothings [
https://en.wikipedia.org/wiki/Know_Nothing]
New York has a lot of Irish and even more Catholics. We've also got a lot of Democrats, Liberals and Socialists. If you're goal is to unite like-minded supporters, you may want to consider the types you'll attract with a Know-Nothing as your logo.