@Why should we fall out with the US?
"Yeah, we need Galileo because we trust our European colleagues so much more than the US - NOT!....
....Since then we've been pretty much the best of buddies, and far better than with any European country."
Just because we're not shooting each other, doesn't mean we're mates. They may be all smiles in public, but do not think for a minute that the US cares at all about the UK beyond how it can be used to further US interests and vice versa. Hell, the only reason we have nuclear weapons is because, after the yanks nicked our research, they basically told us, "We have the bomb. You will all do as you're told." We had to build our own before they'd treat us as anything more than some locals who annoyingly live next to their airbases.
However, you're unlikely to appreciate the subtleties of geopolitics since you've used the phrase "anti-Americanism". I must admit that it's a fantastic PR job - which other country has managed to stomp around the world telling everyone to bow to their will and, at any sign of dissent, claim that *they* are being treated badly? Truly masterful.
To put that in context, would you refer to the diplomatic rumblings about Iran as anti-Iranianism? No, thought not. Subservience to the US is clearly your default setting - how else could you conflate a socialist revolutionary and a religious extremist who wants to create an Islamic caliphate. Oh yes that's right, their biggest defining feature is being "not-American".
You've bought in to the false dichotomy of "with-us-or-against". Well done, have a Big Mac.