I think it's pretty universal across Europe that people are moving more to the extremes. But that doesn't make the original parties suddenly "centrist" -- they're just status-quo, "old school".

Centrist governments are trying to use "hate speech" laws as a way of curbing their loss of control of the media

I'm sorry, but this just sounds like populist propaganda. There hasn't been government control of the media like you suggest; instead, the media used to be civil. The current "popular" channels do away with civility, and any voice critical of that tone is immediately discarded by playing the victim, like you are doing here.

The establishment, still representing the civil masses, is perfectly within scope to try and curb uncivility. Whether their methods are effective is up for debate, but the goal isn't -- we all know what happened last time Europe went uncivil (80 million premature deaths).