It's certainly not that, other apps that use only public APIs that don't show ads (e.g. Apollo) are specifically acknowledged and allowed by Reddit admins.

The speculation in the thread appears to be that this is triggered by a part of the app that is not using the public APIs.

But also, I'd bet that this is just FPs from anti-abuse, not some kind of ad blocking conspiracy. Somebody sent a lot of spam using the chat feature, and the fingerprint of that traffic happens to match the fingerprint of this application. And rather than combine both signals derived from the chat message content and from fingerprinting for issuing their bans, they just used the latter.

I've been using Baconreader for a long while and it has no Reddit ads.