I think this makes sense actually... there are degrees of relative closeness among "personal" friends. I know in my real life I have personal friend who (not that... or is it whom?) I feel are more distant than others.
There are close friends vs. regular friends, I agree.
"Whom" is a funny one, because using it correctly can sound stilted. In your sentence above, "whom" would actually be correct. It's
"I have a personal friend whom I call every week."
but
"I have a personal friend who calls me every week."
In other words,"who" is the subject, doing the action, whereas "whom" is the object being acted upon.
So in grammatically discerning audiences, I try to use the correct form. But if I'm talking to a friend who says "The boss talked to Sally and I," a friend whom I love despite their use of less-than-perfect grammar, I might use "who," even knowing it's incorrect, because "whom" can sound so highfalutin.
Here's another one that's widely misused: lay/lie. As in "Why don't you go lay down?" or "I have a personal friend who I think should lay low for a while."