After more thought, care for sounds less personal to me. It reminds me of being taught as a child that if I didn't like a food or activity, I should say I didn't care for it, rather than that I didn't like it or hated it (which sounds pretty pompous coming from a child, but whatever). In that context, care for meant general approbation, not a specific inclination.

But for T's, I can see many using these expressions interchangeably.