People swapping sides on an issue in a debate team setting seems natural, but people swapping sides in an anti-offensive discussion seems rare.

Unfortunately, "people swapping sides" basically never happens in highly factionalized debates: at some point, the adversarial mode degrades into "debate as war/struggle", with no redeeming sportmanship. I think this is something that the sensitivity mode might be able to guard against. Even "taking offense" is not wholly unproductive after all: we should keep in mind that there are many issues that people physically fight over. Even leaving the issue of shared notions/values aside, the sensitivity mode seems to be much more open to "political" mitigation efforts such as mediation, compromise and conflict de-escalation.