The implication is that there does not exist a gradient between (or even orthogonality to) left and right. If something is just a little bit short of left, it's considered a "dog whistle", implicative that it's all the way to the right now.
I know a lot of people who have voted blue their entire lives that are against cancel culture btw.
No, people should be allowed to do as they please (assuming they aren't abusing the earth or other living beings), and boycotts are a useful tool for change.
But it's becoming the first tool people reach for, and that's not healthy. Kind of how force is sometimes necessary, but should be avoided as much as possible. Someone who jumps to force immediately is a scary person to empower.
Also, there is a noteworthy difference between boycotting something you don't like and boycotting whichever power is capable of cancelling the thing you don't like. It's definitely necessary at times, but it's not a great means to an end.
My mother read me this book as a child (https://en.wikipedia.org/wiki/The_Butter_Battle_Book) and the fact that overt force will be met with greater overt force until someone hits a limit (and nobody really wins) has stuck and has been very consistently reinforced in my life. I see cancel culture as pretty obvious show of force and no matter how much people might inflate its victories and minimize its short-comings, I see it netting out to roughly zero. It really just enables worse behavior on both sides.
The truth is, it's only "Cancel Culture" if it's against something they like
To claim it implies a lack of a gradient is a bit of a slip given the absense of left wing practice of it and looks a lot like projective assumptions "everyone steals" from a serial thief to claim it is unfair they are the only one arrested for stealing.
Maybe we are all affected and should try to just judge things on their own merit, without looking for which side they belong to to..