I’m registered with BC and Vave for playing with crypto. When you register you don’t have to give any details other than your name and email address as its a crypto site.
I personally wouldn’t worry I’ve been with them for over 6 months and never had any issues with my details getting leaked as far as I’m aware. As for in the right as you said they are un regulated and are not obligated under the same rules as UK casinos, but from my experience the chat are helpful so I’d ask them.
Hope you get what you need sorted.