Aren't these ... just blueshifting the colors back to a visible light image, which is how they would look if they were moving at the same relative speed as us?

Aren't these ... just blueshifting the colors back to a visible light image, which is how they would look if they were moving at the same relative speed as us? No. There are basically two things influencing the colors of galaxies, their age (young ones have bright, blue stars, old ones are more red) and their distance. In the first "unveil" image of the gravitational lens, you can find several extremely red objects (that are completely absent in the HST images if you do a side by side comparison). These are likely extremely distant galaxies where the "blue"/"green" bands in the JWST image (and all the HST bands) are very faint because it falls in the extreme UV in the galaxy's rest wavelengths.