"But Trump" doesn't really work here. https://www.washingtonpost.com/lifestyle/style/palm-beach-used-to-be-a-nice-town-for-billionaires-then-trump-came-along/2019/01/08/a14b1708-1049-11e9-84fc-d58c33d6c8c7_story.html
"So Trump opened Mar-a-Lago as a private club in 1995. Unlike the Everglades or Bath and Tennis clubs, which did not admit Jewish members, and the Palm Beach Country Club, which admitted wealthy Jews, Mar-a-Lago was open to anyone. “Basically, he didn’t care who came in as long as they could pay for it,” explains a Palm Beach social expert. Money may have been the motive, but Trump’s open-door policy — his was the first club to accept African Americans and openly gay couples — began the slow process to diversify other clubs in town."
To the question at hand, it's a private club and they can do what they want. Given he's a Dem he'll get away with it (and apparently the two other all white clubs he's a member of). If he was a Rep he'd be getting slaughtered.