Do they have the right to bar you? That seems unfair!
Nevada casinos have the legal right to "refuse service to anyone", meaning they can decide not to deal blackjack to people they have identified as advantage players. Surprisingly, this fact turns out to benefit blackjack players. Casinos can afford to offer great games - beatable games - to most customers because they reserve the right to bar the most blatant advantage players.
If the casinos couldn't bar anyone, they would be afraid to offer a good game of blackjack. Instead, they'd either stop offering blackjack entirely, or they would offer a lousy game such as the one found in Atlantic City.