I've read the material Dr Chris Oakley has on his internet site. He criticises QED on the basis that renormalisation is a fiddle to allow calculations to be made. He does not say is he thinks Feynman did not deserve a share in the Nobel prize in 1965. I suppose that the answer would be that even if renormalisation is an illegitimate short cut, it works, and if the boots fit you should wear them.
Anyway, Feynman came up with the conceptual calculating scheme, the Feynman diagrams analysis of for sorting out what interactions are possible and for identifying the most significant. This has uses generally in modern physics and nuclear interactions that are well beyond the technical calculations of the 0.116... % increase in the magnetic moment of an electron that is due to virtual particle couplings.
It would be nice for Dr Oakley to try to come up with some more tangible (causal) mathematics for QED if he doesn't like renormalisation. The love for abstract mathematical theorems, and the need to force-fit them to a reluctant physical universe, smacks of crackpotism.
On this subject, it is interesting to compare quacks with cranks. In medicine, quacks are people trying to profit, in a get-rick-quick way, from selling bogus or at least not properly proved, treatments. Dr Motl recently pointed out a book on Amazon which claimed to solve all the problems of physics, and which on its internet site turned out to be just political. It had a 5 star rating on Amazon, and was welling well. This seems to be to be quackery, not crackpot.
The problem with this is that these people, who are better at marketing but less good at science, make the going tougher for those of us who are really concerned with doing something positive. Crackpot is a term for unfamiliar ideas. It is not the same as quackery, which is making money under somewhat misleading pretenses.