Yep, as @User says, best to try and explain what outcome you want and someone in here will be able to give some advice on a good policy set up to use.
You can make a public table private to everyone, turn on Row Level Security and have no policies.
supabase-js (with the anon key) won't be able to do anything with that table then.
but, you miss out on all the magic of supabase auth policies then 😦
and you'll end up having a backend doing the work for you when you could be fetching/writing to a table directly from the client.
i'm guessing the use case you actually want is that a user (tim@apple.com) could read their info from public.private-profiles, but nobody else can have access?e