I think at a private club, they can set the dress code however they like.

If you're a public course, looking for public dollars, to some degree you have to accept public dress.

I've played plenty-a-around in a tee shirt and jeans at my local course, but when I travel, I've always got khakis and a golf shirt ready to go (in case someone balks at my tee shirt).

And I wear a fedora, regardless.