It is possible to trust someone professionally and not personally?

I’ve connected with a guy who I mixed feelings about.  I like him, but there is something about him I don’t like.  I haven’t figured out what it is.  Anyway, because of his love of business, I know I can trust him professionally.  Due to some things that have happened (not really bad; not really good), I don’t think I could rely on him personally.  This is a strange feeling.

So, is it possible to trust someone professionally and not personally?