Is adding links to artist's personal Facebook profiles accepted?

No.

It isn't? I would've thought that it would be okay to add their personal profiles on the artist pages. I think I've even seen artist pages with links to their personal Instagram account.

Information should only be added to the database when it is publicly available AND connected to the artist's work as an artist. Unless the artist explicitly consents to their social media accounts being added to their artist page, usually because in those cases it's not a personal page so much as a promotional one, then the preferred action is not to include such links on MA.

We're not interested in digging up the personal lives of artists; just the information they've made available to the public in their role as artists/musicians.