They can, but conservatives don’t do things like that.
And if those clubs are smart, they won't say a word. I am a conservative white male, but if you looked at my resume from Law school organizations that I belonged to, you would conclude that I was a liberal black female. I had a lot of fun and we all got along pretty well. Having said that, I did go to a pretty conservative law school, e.g. the president of the Environmental law forum loved fox hunting with all the bells and whistles (horses, hounds, horns, etc...). And yes, she did look pretty good in her "whites and reds."