Do red blood cells have no MHC? (I have often heard that they do not.)
If so why are they not destroyed by immune cells?
They do not, at least not normally or noticeably. MHC I occurs on all nucleated cells, and red blood cells do not have nuclei. If they did indeed have MHC on them, blood transfusions would be as successful and as tricky as organ donation. There are reports of MHC detection on red blood cells, but the amount is orders of magnitude smaller than elsewhere, only present for certain MHC alleles, and often transient.