I think it is a difficult question to answer if the difference between Obama and Trump seems about as arbitrary as choosing a sports team because it's based in your hometown.

Even though it is relatively new, I think moral foundations theory[1] is an excellent place to start in understanding how people assess moral choices that underlie political preferences. With imagination, try to understand how it is impossible to maximize the fulfilling all of these goals he describes simultaneously, and how the moral foundations inevitably come into conflict. Also, try to imagine how different people you know might prioritize one over the other.

For example, nearly everyone wants to claim that they are loyal to people they know well (people in their group) and nearly everyone wants to claim that they are just and would not harm people indiscriminately. Yet clearly people prioritize these two goals very differently. For some almost no inconvenience to others is too great in order to offset even the most minor risk, and for others almost no danger is great enough to justify the most minor inconvenience to strangers.

Hopefully, that sheds a little light on the idea that people have different fundamental goals.

Next, one might explore how effectively different policies achieve different goals. An example could be the topic of trade barriers. How will they affect total world economic production, or the economic production of individual countries relative to each other, the impact on total economic output within one's own country, and how that economic output will be distributed among different groups of people within the country.

And perhaps finally, how will people make their political arguments, given that the people who make political arguments are likely to at least have some intuition about what is likely to convince different types of people. For example, if you want a distribution of wealth favoring the top, then you'll likely talk about how a meritocratic system increases overall economic growth for everyone, rather than only just saying that you think they deserve it. And, if you want a more equal distribution of wealth you will probably talk about talent discovery from a larger pool of people, the value of social safety nets in encouraging entrepreneurship, or the inefficiency of workers who are made to struggle, rather than just saying that everyone deserves a moderate standard of living regardless of the talents they were born with.

Anyway, if you've never supported Trump, but don't see how his decisions have been different from Obama's it could just be that the overwhelming majority of people you know are negative about him, just as other people might never have supported Obama or Clinton because people around them complained about them often. Maybe one way to figure out what you would believe independent of peer pressure is to identify the different values politicians appeal to within a single party. Partly because people in Congress have very different constituents, it can be striking how much a people who seem unified within the same party are appeal to radically conflicting values.

[1] https://en.wikipedia.org/wiki/Moral_foundations_theory