I can "like" a wide variety of people.
If they are interesting or funny enough, I am even willing to put up with an extremely selfish person, to some extent. In the latter case, it's kind of like the old stories about always remaining within the circle when conjuring demons. If you know that this person takes their time and scheduling commitments lightly, for example, do not even try to get their agreement to meet you at a future date.
The Dale Carnegie-type books say that we like people who show an interest in our favorite subject -ourselves. I think there's a lot of truth to this. Having some common interests or goals can help this phenomenon to not seem so disagreeable, if indeed you see this as "false".
I also like people who can smoothly change gears between being good listeners and good talkers. Creative people. People who are open to suggestions, assuming they seem to lead a life which ( to me, or to both of us ) seems boring or otherwise objectionable when I am meeting them. Sometimes I am student and sometimes I am teacher, even with children or people one would not otherwise think to be "teachers".
I like some people whose skills and strengths complement mine vs. mirror them.
It is not necessary for me to "like" someone to spend occasional productive time or even enjoyable time with them. This assumes I can subtly or directly take some charge about when or how often I interact with people I don't like, though. I can feel the opposite way when I am stuck dealing with such people at their convenience. I can often change the behavior of people who were originally unlikeable by me. Or I can at least get them to change it temporarily ( while they are with me ) by making sure that during those occasions we engage in activities that we find mutually beneficial.
I have even been known to take on clients that were obnoxious, just because they paid well. One must always weigh the pros and cons of this kind of thing, to constantly update our evaluations of whether it is worth it. ( And weigh the cost of time spent evaluating, too, which is a secondary aspect sometimes not considered. ) I have friends and associates with the complete opposite POV on this latter point. They will not take on clients unless there develops a really strong warm/fuzzy sense of "win-win" in early meetings. I continue to question myself as to whether I should change and begin doing this myself.