Liverpool isn't racist, that's nonsense; don't let that turn you off. There are assholes with every club. (although supporting them because of the ownership is a kind of weak reason too, imo)
Supporting two teams: In your own league I would tend to say it's not "ok", but in a foreign league without having cheered and suffered with a specific team for years, I don't see anything wrong with it.
I would say just watch matches you're interested in every other week and fondness for one club or another will grow naturally over time.