Apparently, that is a prerogative of only group Y nowadays.
But what seems problematic for me is when institutions react to random outrage groups (which often are very vocal but small groups) on social media by blindly joining in the outrage and rapidly severing ties with people (firing them, removing authors, etc) without a serious investigation of what - if any - actual wrongdoing there was, what were the circumstances, etc. I would expect some semblance of due process instead of "just" doing what the crowd says immediately for PR reasons.
Joss Whedon is a showrunner and filmmaker, of Buffy the Vampire Slayer fame. A few years ago while going through a divorce, his ex-wife alleged that he had sex with female staff on one of his shows. This lead to allegations that his demeanor on the set of Justice League was snide and unprofessional. Which lead to former Buffy and Angel actors coming forward, and alleging that Joss called an actress "fat" when she got pregnant almost 20 years ago.
James Cameron is a filmmaker of Titanic and Terminator fame. He has been married five times, notably to filmmakers he's worked with and actresses who worked on his films. Some of his divorces have been attributed to affairs with other actresses under his employ. He is a notoriously angry and difficult director to work for, and on the set of The Abyss he was punched in the face by an actor who was nearly allowed to drown because Cameron didn't want to spoil the take.
Joss Whedon is effectively canceled. He has been forced to step down from a new show he was developing for HBO, and his fanbase on various Internet forums has viscerally turned against him.
James Cameron is an Academy Award winner, one of the most marketable brands in the entertainment industry, and everyone will be lining up to watch Avatar sequels over the next few years.
For me personally, the inconsistency and near-randomness of it all is just... unsettling.
-- Context is irrelevant. People are being canceled for using the wrong word when enumerating words which cannot be said. again, some people can say them, some can't.
-- it is completely out of proportion to things which do actual damage. This really bothers me. Someone saying something really bad means less to me than even the mildest act of violence
-- some places are upping the ante to claim that speech is actual violence and that if certain people aren't fired, then the workplace is unsafe