I agree that its implicit values are generally egalitarian, or at least aspire to be egalitarian, but I don't think there's a clear left-right split. My concern is not that we shouldn't be egalitarians. I'm a socialist; my avatar is named after a famous anarchist. It's that there is a culture of debate - 'cancel culture' - that betrays several flaws.
Should we value debate and engage with those we disagree with or ignore their arguments and ostracise them? Should we persuade those we disagree with or tell them they're horrible people? Should we address ourselves to the causes of prejudice and small-mindedness, or retributively punish those who misstep? Debate, persuasion, and opposition to retributive justice - those are scarcely values that are the monopoly of the right, and indeed, the last one runs counter to the right.
You are focusing on 'easy cases'. You write, 'you're saying that we need to welcome, broadcast and hire people who we genuinely think are vile and awful?' But that presupposes the precise crux of the debate: whether most people targeted by 'cancel culture' really are, as you say, 'vile and awful'.
You say we should encourage the firing of 'violent racists'. I think that's a reasonable option, depending on the context. But that's an easy case. The kind of problems I highlighted are found arrayed against people of all political stripes, often for minor offences or errors.
I was reading a large number of people abuse a Guardian journalist this morning for including the owner of a Pizzeria in a write-up of how working-class life has been affected by COVID - a mistake, for sure, even a humorous one, but not one that should be met by abuse. The owner in question was being doxxed, and his restaurant down-voted on review sites. To me, this kind of case is entirely typical of cancel culture, not anti-fascism.