I don't know the full situation in Canada or the US, or how well Left v Right issues align with Left v Right issues in the UK.
First off, there are some dangerous individuals on the Right. They often spout racist language and are often violent. But we have laws to deal with them and, in the UK at least, they are marginalised and fractured, thank goodness.
Then there's the Left. These people have infected our schools, town halls, universities. They hate capitalism and secretly or otherwise despise democracy. Many have personal histories of supporting communism and sympathising with the IRA. They sneer at free speech, unless free speech is used to further their agenda. They have seemingly decided to team up with Islamists - 'my enemy's enemy is my friend', etc. - which means that the same people who championed gay rights in the 80s, now invite to speak Islamic speakers who preach death to homosexuals.
There's a similar story to Prof Peterson that happened in the UK: some well-known professor who had contributed much to science made a sexist but relatively harmless comment ('women make poor laboratory researchers because they fall in love with their male colleagues', or similar). Basically harmless - an apology could've sorted it out. Or it should have been allowed as free speech. This professor lost his job because of one crappy little joke - the big online 'outrage' by leftists, the professionally outraged and other cancerous polyps on the anus of humanity got him fired. He became persona non grata. I don't know if it ruined his entire career.
That whole episode was despicable - DESPICABLE.
And these SJWs have no democratic mandate. They just shout the loudest and have managed to infect our public institutions.