I am not British, but instead American. I can tell you that approximately nobody cares about a symbol hanging in the House of Representatives. There are plenty of problems and controversies in US politics, but this is not one of them. Further, Latin has no political cachet in America. None of our politicians have studied Latin in ages, and you never see it used in political speeches. Nor do you see classical references made by politicians: none of them are referencing classical myths. I think you're projecting these aspects of British education and culture onto America.

Also, it's very obviously not the case that studying classics makes you imperialist. I don't doubt that some right-wingers may like to add classics into their educational program, to create a link to the past, as you say, but that is not inherent in classical studies.

I studied classics (mostly Latin and Greek) at the university level, and not only was the phenomenon to which you refer not obviously part of the teaching, it wasn't there in the first place.

In any case, the problem isn't the substance of studying Latin, or studying history of any kind for that matter. It's about people who already have right-wing views liking to use classical aesthetics.