Re: Is light leaving a high gravity object redshifted by its gravity?

Yes, but the effect is largely not significant.
The doppler shifts of distant galaxies are measured
by observing the spectra of the superimposed light
of billions of stars.  Almost all of these are
main sequence and giant stars, for which the gravitational
redshift is about 1 part in a million, or less.
White dwarf stars produce light redshifted by
about 1 part in 10000, and neutron stars by roughly
20%, but light from these stars does not contribute
much at all to the overall visible light emitted
by distant galaxies.