Adding you both, this touches BRIN and GiST. Here is the short version so you don't have to read the whole thread.
One box with a NaN coordinate gets into a BRIN or GiST union key, and no box operator is true against a NaN bound. So the whole range or subtree holding that box disappears from index scans. KNN searches with a NaN in a key or in the query point fail with "inconsistent point values".
v6 from Sep 28 has four patches. 0001 fixes BRIN with a box_mergeable support function, master only. 0002 fixes GiST union keys and the ~= case. 0003 is Kirill's NaN point check for polygon and circle searches, it also corrects a count in create_index.out where the index scan has returned 4 and the seq scan 5. 0004 fixes GiST KNN. 0002 to 0004 go back to 14 with small rebases. For the back branches the BRIN fix is v6-REL_18-0001, the scan checks whether the union contains itself, no catalog change. That check would also do for master if you would rather skip the catversion bump. Old indexes return correct results without a REINDEX with either approach.
Manu compared seq scan with index scan for every operator of the box, point, polygon and circle opclasses, 6769 checks on master. Every mismatch goes to zero except point <@ polygon with a NaN vertex, which is a heap bug in point_inside() and gets its own thread.
