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!
True! For example, I inherently have a bias towards wanting LGBTQ people to have the right to participate in society through marriage, anti-discrimination laws, etc because I'm LGBTQ. I suspect a lot of black people have a bias towards wanting anti-discrimination legislation so they don't get discriminated against, too.
Does that strike you as unreasonable?
(i'm not going to pretend that i'm always cool, calm and collected in real life. far from it, i'm as flawed as the next person. but when it comes to thinking about this stuff, and striving to be more consistent with my own principles, this is the way i think myself out of all the partisanship i see around me.)