In one of his letters Einstein says: "If the speed of light is the least
bit affected by the speed of the light source, then my whole theory of
relativity and theory of gravity is false".
When will the speed of light depend on the speed of the light source? When
light moves as a particle. It is as if the source emitted a bullet - the
speed of the bullet (with respect to the source) is added to the speed of
the source. This is sometimes called Newton's c+v theory, in
contradistinction to Einstein's c theory.
All evidence, both theoretical and experimental, speaks in favour of the
c+v theory. Light is proved to move as a particle in the blackbody cavity
and there is no reason in believing that it moves as a wave elsewhere.
Einstein himself claims that the speed of light is not constant in Section
22 in his "Relativity". Michelson-Morley experiment confirms the c+v
theory. Even the redshift factor confirms the c+v theory and refutes the c
theory (see http://www.wbabin.net/valev/valev3.htm ).
The fact that the obviously wrong c theory has been worshipped for 100
years suggests that physical science has been converted into a cult -
perhaps one of the most dogmatic cults in the history of mankind.