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.
There are other histocompatibility antigens on the surface of blood cells, e.g. A, B, Rh, etc... (There are probably a lot more which change less by person to person, so they have lower effect on the outcome of blood transfusion.) These antigens can be recognized by immune cells as self, that's why they don't destroy them. Before complete differentiation RBCs have nuclei, so they can have MHC1 remnants on their surface from that period of their development. RBCs are relatively well tolerated by the immune system especially with coverage.
you are right.red blood cells do not have noticeable MHC 1 molecules.But rather the have high levels of CD47 markers which are recognized by the immune system as self.On the other hand red blood cells during development are nucleated they may contain small traces of MHC 1 molecules.I hope this answers your question.