It is against facebook terms of use to create a fake profile. Meaning it would be extremely unethical and possibly illegal for a therapist or any other professional to create a fake profile to look someone up. It is questionable for someone to use their own profile for business use in order to get info on another person. It is acceptable to view public facebook information which doesn't require a login.

This is information straight from an attorney who sets the standards for how I can go about locating people in my line of work (not behavioral health, but social services related).

That being said my online therapist has a business page. I liked it. She said "I saw that, cute dog." I had a dog as my profile picture. If she looked beyond that I dont know however I think the implied consent would be there, since I liked her page, that I give her permission to view mine from her business page.