Edit: My problem solved!! thx to @Joonas for creating the script https://gist.github.com/joonaspaakko/013a223e94ba0fb9a2a0?permalink_comment_id=2771421#gistcomment-2771421
I wouldn't use a clipping mask here. I'd use a Layer Style.
You can apply an
Overlay Layer Style to the group
This essentially provides the same result as using a clipping mask.
If you want each layer within the group to be individually colored.
Effects item in the Layers panel and choose
Copy Layer Style. Then delete the style from the group.
Then highlight all the layers in the group in the Layers Panel, right-click and choose
Paste Layer Style.
You can then adjust the layer style on any individual layer to tweak any coloring specifically.
If you're dead set on using a clipping mask, you'll need to duplicate the mask for each layer, then merge the clipping mask with each associated layer. Of note, if you use the
Create Layer option when right clicking a the Layer Styles, you'll see that the overlay Layer Style actually expands to be a clipping mask on the layer (Which You'd need to merge as well to "bake in".)
Here's something simple, although just not as asked.
I have letter A as a layer group. The three lines of the A are separate layers named to Part 1, 2 and 3. Every part contains mostly grey, but also black and white to show they will be not colorized. The layer group has blending mode = Normal. Mode "Pass through" wouldn't keep the color inside the group.
Colorization: Adjustment layer Hue/Saturation with option Colorize=ON makes all non-black and non-white blue: