"[adjective] and [adjective] [noun]" -- Should the noun be singular or plural?

The first sentence features ellipsis, that is, the omission of elements which are recoverable from the linguistic context or the situation. A full version would be on both the sender side and the receiver side. Once we reach the end of the sentence we can recover side and place it in our minds after sender. That’s not too difficult to do because the missing element occurs within a few words. However, some readers might be uncomfortable in performing that little bit of linguistic gymnastics, and that is presumably what the reviewer felt.

The answer to your question is that both sentences are grammatical, and both convey the same meaning. If you think your readers might have difficulty with the omission of side after sender, then use the version that uses the plural: on both the sender and the receiver sides. Alternatively, use the full version of the ellipted form with the singular: on both the sender side and the receiver side.

From a native speaker:

When you say "There is only one sender side and only one receiver side" that is by definition plural. There are two sides. Use the plural.

When you suggest "The green and the blue box are standing on the table" (instead of "boxes"), that is not correct English. One box that is colored green and blue is "the green and (not 'the') blue box is..." Two boxes would be "The green and the blue boxes are..."