Canada here (Ontario really, probably varies by province) - our mayors and city councilors are politicians but they're explicitly forbidden from running as part of a party. Which I honestly think works so well it should be extended to all levels of politics.
Famously, the US founding fathers warned against the dangers of political parties, only to see them spring up in the US anyways. You really need to design your political system carefully so that there is no incentive to form political parties. I don't know if anyone has ever successfully done this. People should be thinking about it more though.
Specifically, I think a political party happens when two politicians make a bargain that they will each vote for some of the other politician's policies. They don't have to call it "the X party" for it to be a de facto political party.
There are some offices which are designated as nonpartisan here in the US too, I think they are typically offices which don't have a lot of scope for this sort of bargaining. If they did have scope for such bargaining, I wouldn't want to rely on the honor system in the long term. I would want to codify it into law somehow. But how? The best way is probably to reduce the incentive for striking bargains somehow? Again, how? Or maybe bargains are just a distraction, and the real problem lies elsewhere? As I said, people should be thinking more.
The warning about factions wasn't to avoid them. It was that with humans factions are inevitable. The argument was to design a government were the power of factions are minimized or pitted against each other.
In Canada's largest city the mayor is firmly and strongly associated with the NDP. "Chow served as the New Democratic Party member of Parliament for Trinity—Spadina from 2006 to 2014."
And yet that was not the central in her run for mayor at all (I live in that city). She campaigned on policy, not on party branding, like every other candidate did.
