FWIW I'm not saying this is a good thing, or purposeful, but just that if the goal was to eliminate dissent, a whole bunch of people quitting is probably more or less accomplishing the goal.

Product managers are not exactly a time critical position. If the iOS app falls behind the Android app for a few months, will many users even notice?

And it won't take them long to re-fill these roles. There's a ton of unmet demand to work at a place that's purged the activists. You aren't gonna see them much on Twitter but Basecamp just gave themselves a massive recruiting advantage that FAANG cannot/will not match, and they already had a good reputation. Lots of people read DHH's blog post and thought "excellent, that's what's needed". Any impact on the firm will be transient at best.