The distinction between members only and anyone confuses me tbh. You can access members' profiles, assuming they've chosen to make it visible in their settings, by clicking on their username. Alternatively, you will be able to see their new profile posts under "New Profile Posts". But, if you don't have an account (and you can obviously test this by logging out) you simply can't click on usernames, and the "New Profile Posts" tab doesn't appear for you. So there is no way to see profiles, even those whose visibilities have been set to anyone. I thought that perhaps one would be able to access these profiles with a direct link but after testing it out, this doesn't seem to be the case either.
TLDR: It seems that even if you set your profile visibility to anyone, non-members still won't be able to access it. So you don't have to worry about anything.