People really have to differ between rooting against or for people from a certain country and actual like or dislike for it. I'm Austrian so in football I'm always rooting against the Germans. Always did, always will. My grandfather taught me so and so it has basically become a tradition.
Does that mean I have a genuine dislike for Germans? Of course not. It's just that sports often get very boring if you don't have something to root for.
Now I'll admit, Britain and cycling are a bit more complicated as nationalism usually isn't as big a part of it (or at least for me it never was, guess only rooting for Austrians would also be sorta depressing) but I guess it is the very fact that Sky has made cycling about nationalism many cycling fans don't like. If you have a forum that is very multicultural and where the standard is that people root for riders completely independently of nationality, fans who only root for someone for that one reason strike out. In fairness, there are those "nationalistic" members from other countries as well, but it's the quantity in which they suddenly appear when Froome/Thomas/Wiggins do or did well that often annoyed the other forum members who felt like these people weren't actual fans of the sport.
I also think people often confuse disliking Brits with disliking Skineos. I never felt any sort of dislike for the Yates twins and felt like Simon was actually quite a popular Vuelta winner in 18.