No they don’t, this is why Boris Johnson gave up his American citizenship.

(https://www.ftadviser.com/content/7fdbf645-1cc6-5f78-b01b-10c9c9eff904)

See how nazi coopted skinhead culture -

https://allthatsinteresting.com/skinheads-history

It not too wildly different to how it works today… Gamergate being a great example.