I agree with you this is greatly exaggerated by the US right wing - along with much else about the UK.

However, there are serious issues with hate speech laws. They go a long way beyond preventing abuse - threatening behaviour and similar were illegal before hate speech laws were passed. What hate speech laws made illegal were things that were not illegal, bit views that were judged unpleasant. We also now have criminalisation of behaviour such as silent prayer, or offering help in the wrong place.

On top of that we have "non-crime hate incidents" where the police investigate and record people for doing things that are legal.

IMO it actually helps racist groups such as the BNP as they can hint to the worst of their supporters that they would like to say things that are more racist by the law prevents them, while at the same time not frightening off more moderate supporters by using extreme language.

Racists and xenophobes have a lot of gain from ambiguity. Not only not frightening off supporters from the ethnic majority by being too extreme, but also using bigotry between minorities. There are European immigrants who hate non-whites, there are Islamphobic Jews (a group the EDL works with), antisemitic Muslims and more.