First Past the Post doesn't guarantee complete nationwide hegemony of two parties. There can be areas where the vote is between a mainstream party and a regional party, because the other mainstream party doesn't show up. This happens in the UK all the time.

They don't take a lot, but those seats are enough that the big parties often have to work with them to cobble together a majority.

Nor is First Past the Post the only factor. There's plenty of southern states that have runoff voting. Their last century of state level offices are just as filled with Democrats and Republicans as anywhere else.

The US is unique in that not only are their only two real parties, but those two parties dominate at every level of government.