The observed speed of light is indeed the same for all observers, regardless of their relative velocities. This is one of the fundamental principles of special relativity. However, this does not mean that redshift is impossible or contradictory.
Redshift is a phenomenon in which light waves from a distant source appear to be shifted towards longer wavelengths, or "redder" in color, when observed from a stationary reference frame. This occurs because of the relative motion between the source of light and the observer.
According to the theory of special relativity, the observed redshift is a consequence of the Doppler effect, which describes the change in frequency or wavelength of a wave due to the relative motion between the source and observer. When an object emitting light moves away from an observer, the wavelengths of the emitted light get stretched, resulting in a redshift.
The key point here is that the redshift is not caused by a change in the speed of light itself. The speed of light remains constant regardless of the motion of the source or observer. However, the observed wavelength of light can change due to the relative motion, leading to a shift in the color of the light.
Redshift is an important tool in astronomy and has been used to study the expansion of the universe. It provides valuable information about the distances, velocities, and nature of celestial objects. The fact that the observed speed of light is constant for all observers does not contradict the phenomenon of redshift but is actually a fundamental principle that helps explain it.