I'm American and British and don't recognize those overgeneralizations nor find them helpful. There are plenty of Americans who get more than annoyed and absolutely do not turn everything into US patriotism (see Thanksgiving as a day of mourning) and plenty of Brits who are using this and any Saint day and similar for a party and/or community building.
Also, I did the bike ride parades as a child in the States. Maybe it's because I was very obviously at the bottom, but it always felt like it was all just a display for the local people in power to act like they're doing and part of the community they largely ignore if not sneer at which yeah, can be based in imperialism and xenophobia, or at the least a sense of superiority & acting like the rest of us are fools. American pageants and displays do tend to be different than UK ones, but the apple doesn't fall that far from the tree.
So patriotism and love of your country is different from the US, where there does not seem to be any strong movement if any for a part to be independent.
The independence and separatists movements do get squashed down harshly in the US and don't have the same public acknowledgement as the UK versions as there is no legal way to go about it, but they are definitely there. Rarely is it a whole recognized state - Texas is probably the best known of those, with Cali and Alaska close behind, but the attempts have been taken even up to the Supreme Court to consider it have failed. As stated by them: "If there was any constitutional issue resolved by the Civil War, it is that there is no right to secede." so it tends to be groups without that kind of recognition and so easier for the government to deal with.
Part of America’s patriotism includes the American dream for immigrants and the idea that anyone can become an Americian, and a lot of the racists there want the Southern states to leave the USA. They are more obsessed with being “European” than American.
Sure, there is the League of the South and other Neo-Con groups, but we also have the New Afrika and Chicano separatist movements in the American South as well.
Most of the larger and most powerful White separatist groups are in the US north. Oregon was literally founded to be a white utopia and still has many issues with white supremacy movements with Portland there and Boston in the Northeast often tying for most racist US city. Lot of the white-European only groups centre around the Northwest, not the South.
While the White ones get more attention, many of the separatist and independence movement are by marginalized groups who feel the part of US patriotism about expansion and control is something they don't want to be part of. That and some fighting to get their own nations back like the Lakotah and the Hawaii movements are a significant part of pushing back against the anyone can become American as while that may be true on paper (but no less true than most other nations at this time so not really a unique selling point) most neither feel that or even want it that way.