Switching to another word isn't ceding power to the bad people. It's taking away their power to redefine things. It's letting them have the now-useless word exclusively, which will become associated with their speech, and not the original meaning. The original meaning is reclaimed by using a new not-yet-soiled word for it, and the cycle continues.
But OPs point is broader: if you allow the bad people to just appropriate the symbol as their own, they're going to gradually take over everything. Never mind swastikas; we're at the point where making an okay sign can be misconstrued as a white nationalist gesture, and people self-censor themselves accordingly.
There's also the reverse problem here, where, if you tie such things so strongly to symbols in popular opinion, then loud condemnation of such symbols is used to "prove" that one is not a bad person. For a major ongoing example of this look at Russia with its cult of "we defeated the Nazis therefore we're definitely the good guys".
At the end of the day, it's really just a lazy shortcut. The bad people are bad because of their ideas and actions, not because of their symbols. If we always look at the ideas and actions, the symbols are irrelevant, and we don't have to surrender them to the bad guys' claims.
Do you have a coherent principle that separates one from the other?
No, you are just giving them the power to actually do stuff without looking like they are doing stuff.
As long as they talk the talk, they don't have to walk the walk. You don''t have to actually care about issues, that's what the DEI department is for.
It only works because we're in a society of judging people the moment we see them. Mimicking the language of "bad people" will get that association. I don't think we'll ever truly "fix" that.
* had everyone declare their pronouns
* advertised their segregated black-only event next month
* repeatedly interrupted to chant "trans rights!"
This is a very common cluster of behavior, and I'm not sure what I would call it other than "woke". If there's another word that would be better, I'm all ears. But my experience has been that proponents don't find any word acceptable, because what they object to is the very idea that this is a distinct cluster of behavior. They feel, as the source article says, that each of my bullet points is just an independent matter of respect.
Tattoos can change, too. If I had a tattoo like that, but had come to see the error of my ways, I would have it removed, or if that was too costly and time-consuming (it takes a year or so of painful, expensive, periodic laser treatments to remove a tattoo), I'd have a tattoo artist cover it up with something else.
There's no excuse for keeping a neo-Nazi tattoo if you stop being a neo-Nazi and realize that neo-Nazis are disgusting people.