Looking from the outside, I think US political discourse IS far more hostile.
Britain won't accept things like Politicians being harassed, or one politician calling for other politicians to be harassed (and that's before we even get to anything Trump related).
And the amount of references I see to "civil war" when wandering across anything relating to US politics (i.e. not zero) is disturbing.
Looking at American politics from the outside, I feel like (in most cases), you're lucky if your elected representatives know how to spell the names of common vegetables and know that the US doesn't share a border with Afghanistan.
I think you need to read more into Thatcher and what happened under her to understand why some sections of society reacted like this.
I don't know a huge amount about Regan, but I doubt you can really compare them.
Britain in the late 70s and early 80s had huge issues which Thatcher addressed, but in hugely contentious ways, in some cases destroying entire industries and their communities.
The structural impact of some choices she made are still present in British society even now, decades later.