If you do not submit the kyc data then how will you make an account on gambling site and gamble with your money ? Even if you are lucky to deposit and gamble without the KYC still on the withdrawal they will ask you for your KYC and if you do not complete the KYC data you will not be able to withdraw the amount.
The only precautions you can take is to store / submit the KYC on trusted sites so there are less chances of your data being used illegally or unlawfully. Other than this we have no option but to submit the KYC
You are right that we don't have much of an option for the time being since there aren't any authentic casinos that don't ask for KYC and lets you deposit, gamble, and withdraw your money all without submitting any personal detail, we can see a few decentralized platforms coming out but yet again, we can't just trust any platform that comes out because we know how saturated the market is and there are a lot of scams happening around.
So the best way, as you said, is to only use the most reputable platforms so that if you need to complete KYC verification, you do it with them and your personal data and documents will be safe from being misused or sold and you can rest assured when gambling with the casino if it's trusted.