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?
The issue is well-known on Coinbase. They've been closing accounts linked to gambling sites for years. There are countless threads about it, like these:
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You can't necessarily just use your own wallet as an intermediary. They'll still flag your account.