I don’t think that those defined as “extremists” under the new proposal will face prosecution.
In many ways it is more sinister than that and rather insidious. At least with a prosecution it is all above board and obvious to everyone what exactly is happening.
The proposal is that all government bodies, including universities, will be banned from having any links or contacts with individuals or organisations which the government has deemed to be extremist.
And the definition of extremist will be expanded to include any individual or organisation which is perceived to undermine the UK and its institutions of government.
So someone could a member of a perfectly legal organisation but banned from speaking at a university, for example. And perhaps speaking to the BBC?
It will almost certainly include Muslim campaigning organisations and presumably could also include anyone campaigning for the abolition of the Constitutional Monarchy. And I can’t see how they wouldn’t class abolition of the House of Lords as undermining UK government institutions.
IMO this is probably the most worrying proposal that I have heard from a UK government in a while. Particularly worrying imo because it presumably could be implemented relatively easily and its effects kept below the radar.