When you have 2 yards separated by a fence, the fence is on one of the sides, somebody owns the fence. The saying means that by not picking sides, you still technically pick a side.
It's a metaphor. You don't need to "believe" in them.
From the rightwing side, I support private healthcare, strict immigration laws (I am an immigrant), and the lower value of human life (https://en.m.wikipedia.org/wiki/Value_of_life)
From the leftwing side, I support higher taxes, UBI, public education, public transit, and work camps
Yeah I don't get why people like OP think not being an extremist means you feel nothing about any political ideology or position.
I agree with Democrats on most issues so I vote accordingly, but I'm not under the illusion that being closer to perfection most of the time means anything the DNC says or does has to be gospel, or I have to do mental gymnastics to make my views fit theirs.
At the end of the day they're a political cabal that seeks to sustain itself with more votes than the other guy. For example, they had zero position on abortion until the 80s, when the GOP decided to politicize it. Because the GOP left the pro-choice crowd behind, the DNC scooped them up and added it to their platform. They don't actually care about abortion, they care about votes.
Remember when CoViD-19 was new and everyone was wearing masks until Trump said Masks Bad so now the GOP has to be anti mask mandate? Note how that has nothing to do with "small government" or any other GOP principle.