How do I select all shades of gray?

Other options here in an action that I once made:

Dropbox - Select Near Neutrals.atn.zip

Defaults can be adjusted for pure neutrals.

Create a grayscale similar to the one shown above. Convert it to RGB.

Add it as a layer to the image and then flatten the layers.

Choose the Magic Wand, set the Options bar to Zero tolerance, and not Contiguous.

Click on the darkest value in the grayscale, then hold down the Shift key to add to the Selection as you click on sequential steps in the grayscale. Don't be shocked to precious few absolute grays in an image.

have the exact same RGB values

You can also use the Magic Wand tool set to Point Sample, Tolerance 0, Sample Only Contiguous pixels Off, Smooth Edge Transitions Off. Zoom in on the pixel you want to match and click on it.

you could use the select by color range option and use the eye dropper tool to carefully sample the specific color you want to target in the selection.

here is a video that show you how the color range panel works:

How to Use Color Range in Photoshop CC - YouTube