Sorry, Thomas, but that is not possible. The privacy level you select for any profile (including your own) applies the same to WikiTree members and the general public alike.
If your parents' profiles are public then everyone (members and non-members) can see their ancestors, so people would be able to see your tree, starting from your parents instead of starting from you. I don't know if that's any help for you, though.
I'm not sure of the reason for your concern, though. WikiTree is free to join and anyone can do it, so sharing information with other members is not all that different from sharing it with non-members - some of them will become members soon.