I don't think it's really even about the specific policy.
Note that the "changes" [1] also include "no more committees" (ie, no more feedback/authority/responsibilty except through the line-of-report hieararchy), "no bringing up past decisions you disagree with", and "no more 360 degree reviews" (no formal way to give feedback to your boss).
I think they are basically changes to focus on... "insubordination". Do what we say, do your job as we say it, don't have an opinion.
I think people are leaving because they don't trust or respect or feel respected by the boss, not over a single particular policy -- although in part over how little he cared what his employees opinions were about the policy.
[1] https://world.hey.com/jason/changes-at-basecamp-7f32afc5