I think that the honest and well-reputed gambling sites will do their best to protect the information of the users and they won't use it for any illegal purpose at all. But, I have heard that there are some other applications and sites which have misused the KYC data of their customers. I always recommend everyone to share your KYC data on only those gambling websites which have built up trust and reputation in the industry.
Of course one should never do KYC on those sites if there is no trust. I think giving personal information to those sites that have been running their business with reputation for a long time that would be fine. Also if one plans to do KYC in a licensed casino that too can be trusted. But putting your trust in someone who doesn't have a license to do KYC is risky. A gambler must have a good knowledge with the site before doing KYC. It is important to remember that those who have been surviving in the market for a long time have almost certainly reached this stage by ensuring proper KYC security.
Are you saying that if I have my money stuck in a casino, and the only way my withdrawal request can be processed is by completing the requested kyc verification, I should do it simply because I do not trust the casino?
Well, to be sincere with you, as long as I am concerned, only a very few casinos are trusted, and that is those that have been in operation for long time and still continue to grow even this present time, and of such casinos are freebitco.in, Stake.com and a few others, every other casinos are pretty new and likely untrusted, but because they don't require kyc before user could deposit funds and play, they have users who deposit and play, and upon withdrawal, the casino might ask such user to submit his or her documents for kyc verification, if the user wants his or her money, I believe trusting the casino or not has nothing to do in such matter, the user have no choice but to submit the requested documents for kyc verification or forfeit his or her money to the casino.