Well – I did what I should have done at the beginning I disabled all plugins (related or not) and enabled them 1-by-1. It turns out it was indeed a plugin – PaidMembershipsPro.
In the Advanced Settings of that plugin there’s a couple of settings that sound like they have nothing to do with bbpress, but after removing the ‘Filter searches and archives’ for members only setting the anonymous posts now show to anonymous users. I’ll have to determine the ramifications (if any) of that for other areas of the site.
Odd indeed – it’s driving me batty trying to go through all the code and determine what function could be doing this.
I’ve turned off any other bbpress related plugin I had, switched to standard Twenty Fourteen theme. I then go in as anonymous on a different browser, create a new topic and then I can’t even see the topic I just created (nor any other anonymous person’s topics).
The topic gets created, looks fine and I can see it. It’s just anonymous users can’t see any anonymous posts.