I had the exact same concerns. You can see my post on here from about a month ago or so "Privacy for cardholders" or something like that and another one about "Insurance companies and MMJ" or something similar. I think your information will be private, but I'm not positive. I haven't been thoroughly convinced, but I decided to get the card anyway.
As far as I know the registry can't really share that information, so unless you specifically tell your primary doc or insurance company I don't think they would know.
I have seen a post where a guy was on workers comp and he was told that the workers comp people would find out through the state. So I don't know. Sorry I couldn't help you more definitively.