I can like someone on a personal level that I don't respect on a professional level, and I can respect someone on a professional level that I don't like on a personal level.
("Professional" could be swapped for a variety of qualities)
Once we belonged to a saddle club on base. Generally speaking, most of the horse owners were wives of active duty. Only active duty could be on the board that made decisions regarding the club, so essentially the board knew nothing about what actually went on day to day, other than what their wives told them.
One day a woman I shall call Horse Sense, and another, Precious Flower, had a falling out.
Precious Flower was angry and embarrassed by something Horse Sense said, and decided that she would get back by getting members who didn't like Horse Sense to trump up a bunch of charges against her so they could kick her out of the club. (I had liked PF on a personal level, up until she pulled this junior high stunt)
Now Horse Sense didn't like me, but I saw first hand that she knew her stuff, and was dedicated and ethical (not to mention the stuff being used against her was absolutely untrue). I had a great deal of respect for her. Precious Flower, on the other hand, even though she was always friendly and nice to my face, I wouldn't have trusted with a plastic goldfish.
My husband was on the board. When I told him what was really going on, and that the "charges" were a bunch of rumor and speculation put togther by a group of spiteful women trying to use the board to settle personal vandettas, he said, "You know she doesn't like you and talks crap about you, right? She's not very nice."
"I don't care. This is about right and wrong. She's getting railroaded because they don't like her, not because she did anything wrong. It doesn't matter if she likes us or not, we need to stand up for her."
I wish I could have been a fly on the wall at that meeting. Precious Flower and her conspirators got their butts handed to them.
In the end Precious Flower had a melt down of a temper tantrum, letting her true colors come blazing through, and
Horse Sense became a friend I enjoyed spending time with, despite the fact we had different philosophies.
I guess this story would also illustrate the ability to change your perspective about someone. In the beginning Horse Sense didn't like or respect me, but because of one action, she had a total change of heart.
You can only judge the parts of people that they allow you to see.