The axial Doppler shift has been left out of the relations of relativity for the most part for 100 years or so. The files below show why it is a groupthink and the impacts of that.
Physics does not have groupthink. Right. Just prove the "The Emperor's New Suite" is contemporary non-fiction,I will play the little the child (ok I am a 75 years old one) and I will post these files which are a correction and impacts a 100 year plus group think in physics. (3 are published the others are on researchgate). The last is acondensed summery.