It's true that gambling sites doesn't let you give access to the private keys of your wallet. I have the same plan as others moving out my balance temporarily and stop my gambling activity before August 1 because the sportsbook that I go to isn't segwit ready. They have no plans or anything related about it.
thats actually the best solution to do around this period move funds out to a wallet you have access to the private keys of your wallet
What happens to our bitcoins that are in an account on a gambling site that isn't SegWit ready and there is (or isn't) a hard fork after August 1st?
You could lose the other half of your coins (if there will be a split)which is not good if you have a huge amount sitting in a gambling site.
its not a guarantee that you will lose the other half i think this will be at the discretion of the betting company to decide if they can give us the other split coins, we have to wait and see