I don't think "just stop picking a side regarding abortion, gun ownership, or gay marriage" is a reasonable solution. These are political wedge issues, but they are also legal questions with answers that can affect your daily life. Of course you want it to go a certain way!
If you really do start from first principles (I think “utilitarianism” might be a better example of something that would be a first principle), and you find out that one side of an issue is good and the other is evil, or even if you find out that one political party is a good bit morally better than the other, you’re now back to picking sides. Because picking the right side of a morally important issue is a moral imperative to most people.