How to change color of a shirt to light color without losing details?

There are numerous ways to do this. I usually start by desaturating to a neutral color and then recoloring. Replace Color on a new layer and blended can work. Be sure to recolor any reflected tint in the scene as well.

Is there a better base shirt color to work from to get to such a light color without losing details? I may be able to get a different starting shirt color to work from.

By @ModRebel376708778qch

Generally, a midtone or lighter gray would be an easier starting point to work with than any dark color. A middle gray can contain details without losing them in the highlights and shadows, and of course is neutral so that it won’t shift any color you apply on top of it.

There are a few videos on YouTube about changing colors of clothing. This video is pretty good:

Sometimes using one Channel (in this case Red) via Channel Mixer as the basis of the Adjustments can be useful. 

For changing color of items, I like to use L*A*B* color. Your sample color was 94L 0A 0B, so basically your color is gray and the tone is just altered. In my sample, i set a color sampler to adjust the shirt. I could have used desaturation, but I used curves for everything - better if your target color isn't gray. So after I got the gray, I used the lightness channel to adjust the tone to 94L. First I moved the highlight end of the curve, till I got the 94. But the dark tones were a bit too dark, so I brought up the shadow end of the curve, till the shadows looked decent, then I readjusted the hightlight end of the curve to bring back the shirt to 94L. When doing this, you want to set your color sampler to what would be considered a middle value of the item: you don't want a highlight or shadow area.

Edit: I tried changing the first image from heather navy (not from mauve) to the light color, which is called "cement".