I withdrew them to Mexc (which is not good decision - to withdraw casino funds directly to exchange wallet, as exchange can flag transaction as problematic).
If you first make a withdrawal from the Freebitcoin site or any other casino to your own address and then only to a centralized exchange, it won't change much. I mean, if a CEX really checks deposits and marks funds from casinos as undesirable, they won't limit themselves to checking only the address from which the deposit was made.
But in the case of MEXC, it seems to me that you shouldn't worry about it because this exchange sometimes adds outright scam tokens, i.e. not really bother with any kind of checks.