It's not just the flag, it's a stylized flag blended with the oath. Which is much more political than a plain flag.
A simpler example might be a flag with 52 stars. It's blatantly political, even though it would likely be harder to notice than the hoodie I looked up.
It depends. In Minnesota, wearing any of the items you listed would be considered electioneering if that was a major issue of the campaign.
So if one candidate has made gay rights a major plank of their platform, then wearing a shirt with a gay pride flag would run afoul of the rules. But that same shirt would be allowed in the absence of that specific issue being promoted by a candidate’s campaign.
I'm fine drawing a line for an officer carrying out election duties that goes further than for other people.
They just shouldn't wear anything that puts the election workers in a position where they have to evaluate the political message. I guess that can be tricky if a uniform somehow became partisan though.
There likely is a moderately sized group of people who are opposed to having police, but the real partisan divide is over what sort of policing is acceptable, not over policing itself.
And even that is not really a sufficient explanation of the differences in opinion, it's too simplistic. People disagree about whether police are biased and things like that.
A simpler example might be a flag with 52 stars. It's blatantly political, even though it would likely be harder to notice than the hoodie I looked up.
https://www.pinterest.com/pin/119415827607659191/
(whether that's the exact same hoodie, who knows, but it matches the description close enough)