What idea does the shifting of spectral emissions of distant galaxies toward the red end of the spectrum support

Observation is never used to 'support' a hypothesis or theory.

The hypothesis or theory is a suggested way to explain what

has been observed.

The expanding universe idea has been offered as an explanation

for the observed red-shift of the radiation from distant galaxies.

To this day, it's still the only way we have of explaining what we see.