Yes—use a true grayscale conversion rather than a desaturation effect. In Photoshop, try Image > Adjustments > Black & White and reduce the Reds slider until the red text matches the darker text more closely.

If you have lots of files, an automated batch method is better. A simple ImageMagick command is:

convert input.png -colorspace Gray output.png

That converts the image to grayscale in a way that removes the color distinction. If needed, you can add a little sharpening after conversion:

convert input.png -colorspace Gray -sharpen 0x1.0 output.png

For many screenshots, this is likely the fastest approach because it can be scripted and repeated automatically.