I posted before trying Cura 5.0, which doesn't have this problem, so the problem is solved.
I'm getting a tree support that goes through an object. The object is symmetrical but only one side has the problem. I don't think there are manifold errors, I didn't see any red:
This is a view looking up from below, the left support looks correct but the right support pierces the object.
Here's a view of the lower third, from above. The tree support is running through a wall of the object (which is hollow).
I'm running Cura version 4.13.0 on a MacBook Pro with macOS 12.4 (Monterey). I didn't see any red in the prepare mode,
This looks similar to the bug reported below in 2019.