Author of Pinafore here. Yes, ironically for an app and userbase that is so focused on privacy, things like private browsing, Privacy Badger, adblockers, etc. can cause compat issues with Pinafore.
Interestingly, the reason is (as I discovered) that most of these tools consider cross-origin requests as a signal of a third-party tracker or ad, and therefore block it. Pinafore works by talking directly to the instance's API, and so the instance itself is suspected to be a third-party tracker. ️