The reason a lot of people think Collective Shout are far left feminist, is because ironically they get a lot of support and are boosted by pro LGBTQIA+ far left feminist groups. Part of the reason Collective Shout got enough power in the first place is exactly these kind of far left spaces, such as reddit groups that brigade and attempt to cancel anything they deem misogynistic.
A far left feminist subreddit with over 14 million users in it, was even giving out detailed instructions on how to brigade for, and support Collective Shout. An example here: https://www.reddit.com/r/TwoXChromosomes/comments/1jvjpsr/reporting_the_new_stea... This is also what eventually led to the Itch.io NSFW ban.
Which is ironic now that the pro LGBTQIA+ far left feminists, with their actions now led to banning of the majority of LGBTQIA+ games on Itch.io. What a surprise, when you try to give power to those cancelling and censoring things, it will backfire, and even things that you believe in will eventually be hit. There is more overlap between conservative puritanical feminists, and far left feminists, than you would initially think. And the far left feminists prop them up.
Also it is a perfect example, of why all censorship, brigading, and attempts to cancel are bad. Because it won't stop at things you agree with, it will eventually hit things you care about, such as thousands of LGBTQIA+ games now being banned here.