First of all, just to make sure we're on the same page about maybe one single thing, I don't think anybody thinks the subject of the linked article is cultural appropriation. I sure don't.
Ultimately everything is somewhat of consensus in society, right? I mean, even near-universal truths like "murder is generally bad" or "helping your neighbors is good" are just sort of things most societies kind of agree on.
Sometimes those consensuses (consensi?) change over time. Marijuana was legal for centuries, and then it wasn't, and now it kind of is again.
Sometimes the consensus is crap. In a lot of places there used to be a societal consensus that marrying your 13 year old cousin, or stoning religious heretics to death was cool.
If you've really done the work, and really explored why the groups affected by cultural appropriation think it's kind of a shitty thing to do, and you really just think they're just being crybabies or liars, and you're making an informed decision to disagree then, hey, cool.
Might not agree with you but if everybody put that much thought into things the world would be a better place.
how should that disagreement be settled
When it comes to an issue like this, maybe weigh the cost of giving a care about it vs. the cost of not giving a care about it.
Example: suppose I like to use slur XYZ because it's funny to me, and I think humor is a great way to bridge the gaps between people, and it would be better if we all decided to simply not let words hurt us. (I actually do feel that way!)
But a lot of people from group ABC feel like it's pretty crappy for me to use XYZ.
I could just simply think they're being oversensitive, and keep saying XYZ but like... is using XYZ really that important to me? It's pretty easy for me to stop using a word. That's a pretty small cost. If it might do some good, or at least make somebody else's day better, fuck it. I'm generally happy to pay that small cost.