As a British person I also find this weird. There was a tiny amount of it with Boris Johnson and that was mirrored in the very small cult of personality that rose up around Jeremy Corbyn. But for the most part politicians of all stripes are considered with mild disdain and actual membership of a political party is seen as probably a bit weird.

In America... rallies! Thousands of people actually pay to go and listen to this self-aggrandising nonsense. It's very odd.

In the UK I usually voted for the liberal democrats or the greens because each appealed to my views in different ways. Occasionally held my nose and voted Labour when "get the conservatives out" seemed the most important thing. Here in Aus, when I get citizenship, I will feel even more free to vote for smaller parties because we have preference voting. I can (and do) discuss politics with friends who have different views, though as my friends mostly skew liberal (ironically) this means none of them will be voting for the Liberal Party...