wave interferometers

the working principle of a Michelson-Morley interferometer for the detection of gravitational waves is commonly explained by the fact that the distances to the mirrors in both arms are not measured to be constant in the passage of the wave, leading to a difference in optical path length and therefore to a shift in the interference pattern. but the photon’s wave lengths are stretched by the time-evolving metric as well: does that mean that there’s no net effect?