Someone a while back mentioned there is nothing in the TOS against it. I know with coinbase or gemini.. ppl said they would ban accounts if you send btc from gambling site to coinbase and vice versa.
Where did you heard about that banning accounts issue?
If you are quite hesitant to withdraw from gambling sites and transfer it to binance, coinbase and other. Why don't you transfer your btc from gambling sites to your wallet? I do that many times and vice versa. And from your wallet to binance or other exchanges.
Anyway, is this the one you are referring to about the TOS issues and banning account?
If so, consider my advice to make sure your account will not be banned by a particular exchange.