You're basically arguing that if you have a service open to the public you should give up all control over what is said or expressed there.
No business is ever going to agree with that.
Nope. I am saying that the company if it wishes to serve the public should conform to its user wishes. Where do you see that I am advocating a company giving up control?
A company like google is doing one of two things here. Its either trying to shape the world or its trying to protect its image. It could be both, but for what Im about to say its easier to hold them as split things.
If Google is trying to protect its image then totally fine, but I also will not support that image and will advocate against that and look to do my business elsewhere. That is, if they are pushing the idea that Peterson's ideas are somehow harmful. If they were doing this type of thing to say the Spencer guy who got punched, I would say oh well.
If Google is trying to shape society into what it thinks is "right" then I have a huge problem with that and will be for more adamant in my stance.