When using thin surface representation, I would expect very little difference between cases where only the thickness of the wing is varying.
When using the thin surface representation, VSPAERO currently only 'knows' about the mean camber surface as represented in the mesh sent to VSPAERO. At present, VSPAERO does not use any thickness information when analyzing a wing in thin surface mode.
When OpenVSP creates the thin surface mesh, the thickness has some influence (so we don't get exactly the same results). Mesh points are arranged on the thick surface (before clustering) based on equal arc length. Then, corresponding top and bottom surface points are averaged to find the mean surface.
Consequently, a thicker version of the same airfoil will end up with a different mesh -- it will effectively have more clustering at the LE. That different mesh will result in a slightly different solution.
In particular, it looks like you've considered the wing with a t/c=1.0 -- which seems to blow up in some situations. That should not be surprising, as that is an absurd thickness for a NACA 5-Digit airfoil.
Rob