Can anyone tell me how will centralized know that the funds came from a gambling site?  I'm only seeing threads before that someone claimed their account got frozen because funds came from a gambling site but no proof that the site itself tells their users that's the exact reason. I think there is another reason why their account got frozen and not because the money was coming from a gambling site.

Furthermore, if OP is really worried, then an extra step of using a non-custodial wallet is necessary.