Right wing? Collective shout is not right-wing... It's neither right nor left wing.
Collective Shout is, in my opinion, just a front. People have been looking into it and found that CS has been around for over ten years, has never once succeeded in anything they attempted to do (they have been caught in many lies just like PETA has), has no financial backing, and doesn't even make 1k hits to their website a month. Suddenly, their backing went from next to nothing (none from government, which most organizations get from) to several million dollars. Also, CS is a group of 10 people and Visa and Mastercard would be losing billions on refusing these transactions, so whatever pushed them had to be something more than financial threat from a handful of people. There is clearly another entity at large here.
To add to the right wing comment, this exact push for censorship was detailed in Trump's Project 2025. Whether it is a coincidence or not, however, I can't say, but it is something to keep in mind.