That's an interesting way to frame it, but I don't think it's accurate. It's not good faith disagreement v. censoriousness, it's censoriousness about what. As I noted in the article, most agree censoriousness regarding overt slurs and Holocaust denial is acceptable. And many social justice activists are arguing in good faith. They genuinely want additional things added to the acceptable censoriousness list, and they're straightforward about why (they think it's racist, transphobic, etc.) It's just that the letter signatories disagree with them about that.

You're right that the terms "free speech" and "cancel culture" don't appear in the letter. But "speech" does more than once, as does "The free exchange of information and ideas, the lifeblood of a liberal society, is daily becoming more constricted." That's a free speech argument, not one dependent on good faith/bad faith. And while the letter says "intolerant climate" and "stifling atmosphere," the currently-in-vogue label for that climate/atmosphere--one that many, including letter signatories, use in related contexts--is "cancel culture."