Your question can be answered in one sentence: yes. Yes, that’s the short answer. If they suspect the player is playing card-counting, casinos can ban them from their casino or take them off a particular game, such as Blackjack. They can accept or reject any player and control their fate.
Other than Blackjack, I’ve heard of video poker players who are skilled in strategy and only play on days with promotions. While I’ve heard of players skilled at slots, I’ve only seen a handful.
Other instances of seemingly innocent things include players winning several times consecutively and receiving offers that were withdrawn. The casino thought they had enough comps to withdraw. If they lost again, the comps would be re-enforced. This is a shortsighted decision, as the games favor the casino. This could discourage players from returning, as they might be disqualified revoking their offers.

Recording players’ play at the casino has been prohibited. They were temporarily or permanently banned after a few warnings or sometimes without notice.

Private operators can make these decisions based on any criteria they choose. These stories can spread negative information and make it more difficult for them to win. They will ban any player they believe is giving the casino an unfair advantage.

This doesn’t mean players were banned from saying it. This is a different question. Winners of casinos have been excluded, particularly those who think they can bring down the casino.