If thats the case then these exchanges shouldn't accept funds from gambling sites.
There are no wallets that directly tagged as owned by specific gambling sites so I don't know how exchanges will able to determined if the funds came from the gambling sites. Gambling-related activities were put on the exchange term as a common and usual term that an exchange should have.
We just based on OP's shared information but who knows there are other issues that's why OP faced such problems. It would be better too if OP can name these exchange and the gambling site involved.
That should show you how advanced chain analysis has become, exchanges engage on this to see if you can be a high risk customer and they can choose to accept your business or not, it is a way to protect themselves from hackers and scammers, and while there is nothing wrong with gambling, exchanges prefer not to deal with them because back in the day hackers and scammers used casinos to launder their coins and it seems the current practices of exchanges still reflect this despite casinos adjusting their policies and the fact this is no longer a problem.