I believe this is being followed for the purpose of making everything transparent and not to get into illegal things. If thats the case then these exchanges shouldn't accept funds from gambling sites.
Not all exchanges restrict or prohibit transaction activity on gambling sites, depending on the exchange, I've read the same thing happens, if I'm not mistaken about PayPal transactions to certain gambling sites, prohibited.
As far as I know the exchange will limit or not approve any transactions of funds / crypto and the like against gambling sites, if the gambling site is not registered or official in that country, exchanges are more comfortable conducting trading transactions against gambling sites that have legally defined gambling by their country, that's one of the main points to prevent things that the exchanges don't want their customers for for the sake of safety.
For that the OP must check about the gambling sites you play, whether they are illegal in your country or vice versa, or you contact the exchange team / management asking about transactions about the gambling site, is it safe for them or not.