Can I use grayscale images when working with ImageJ?
There is no evidence that one is better than the other, most likely because it differs from case to case. Neither you, nor your critics, are right. There is a tiny bit of science in a paper on digitizing blots, generalizing from blots of a specific protein (PMID: 19517440), and they use grayscale for no given reason. Come to think, that is the best paper in the field of immunoblot quantification., and it still lacks evidence.

Immunoblot is semiquantitative, meaning it may sort and order bands (and protein amounts), but it fails often at estimating differences and ratios, and may even fail to see differences. Just try your best to find a difference, in the knowledge that if there is no difference in protein amounts, any fiddling with contrast won't create a difference in bands quantitation.

There is almost no difference between color and black-and-white digitized images of an immunoblot. The parts of the blot that are black will still appear in the computer as White = 0, even though a tri-color image file will detail it to Red = 0, Green = 0, Blue = 0. The parts that are nearly black will still be very close to zero.

The only thing that changes a lot between RGB and color is the background.  The background may change, for example, from White = 200, to Red = 190, Green = 190, Blue = 220. There is one consequence of such switching between values for background. (These changes may be induced by switching between grayscale and RGB, but also by altering exposure time etc.) When you use a method where the background gets too close to the blots, the "amplitude" of the blots, the height of the peaks in ImageJ, will be reduced. This loss of contrast should wash out some of the differences between blot bands and lessen support for differences between bands (i.e., for the alternative hypothesis), making you miss a genuine protein difference.

Again, if your blot bands are different enough so that your percent increase / decrease is huge, and your p value is small, you are all set, regardless of the method you chose. Ask your critics to explain your observed differences other than by differences in protein. But if your quantification fails the p test, I think it will be a honest effort, to change the color from grayscale to RGB, or the other way around, just in case your first choice had been the one that dampens contrast.