How to stop nodes being automatically added to a simple queue in Nodequeue?
In case someone else runs into this, I finally figured it out.

In the settings (admin/structure/nodequeue/[NODEQUEUE_ID]/edit), there's the list of "Type" checkboxes. When I originally set this up, I assumed that I had to check those content types that I wanted allowed into a queue. Turns out, this actually seems to auto-add new nodes of those content types. I unchecked all of the checkboxes, and now things seem to work as they should.