Since most people are liberal about some things and conservative about others, how in the world would we go about deciding in any final sense who is a "liberal" and who is a "conservative"?

Rather, let us determine whether a person is acting or thinking liberally or conservatively in regards to a particular circumstance. That might get us somewhere.

Calling someone a liberal or a conservative gets us nowhere useful whatsoever, in my opinion. It just encourages the maintenance of an established prejudice of some kind. (Of course, we've all done that from time to time, but then...we're all prejudiced. So there you are.)