In terms of improving discussion by differentiating between disagreement and offense:
I think that in order for that to work, it is important that offense is treated as valid and worth addressing. First because, as the article points out, offense is often based on valid fears and concerns. Second because otherwise people will feel the need to present their offense as disagreement in order to get it taken seriously.
Admittedly, I wrote this post 3 years ago when I was seeking clarity around disagreement during a wild time. Re-reading it now, in yet another wild time (3 years "wiser" aka having learned how to change a diaper or two), I missed out on compassion for those who are offended. Like you said, if it's important to find a mutual way forward, then it is also worth addressing the fears + emotional lives of those that are offended.
However, it seems to me that conflating disagreement and offense, and in particular using that to shut down discussion, is a symptom not a root cause. I believe that the root cause is that one half of the current culture war has refused to recognize the validity of offense or prioritize the issues that are at the heart of the offense.
As a result, the other side has concluded that conflating disagreement & offense, and using that as a weapon against opponents, is their only option.