Needless to say they're tying themselves in knots trying to find a suitable redefinition* of something that seems perfectly obvious. To my mind, and probably most people's minds, extremism is simply violence or the threat of violence.
Anything else is just free speech or public protest - possibly abusive and ignorant free speech but that's not the same as extremism. If free speech and public protest becomes "extremism", we're on a very slippery slope indeed.
But the government wants to include anything that "undermines UK democracy", an absurdly vague concept that could include just about anything.
Would rallies in support of Gaza be caught in the net? Or attacks on the government? Or trade union activities? All sorts of routine grassroots protest could be outlawed.
Civil liberties groups and lawyers have already pointed out how dangerous the new law could be, but the government is notorious for ignoring expert advice and going its own sweet way.
*The proposed redefinition of extremism runs as follows (new redefinition on March 13): "the promotion or advancement of an ideology based on violence, hatred or intolerance" that aims to "negate or destroy the fundamental rights and freedoms of others" or "undermine, overturn or replace the UK's system of liberal parliamentary democracy and democratic rights."