Well, depends. It does have some basis in science. In fact, one of the earliest known writing that addressed the saying comes from the Bible. In Matthew 16:2-3, Jesus is quoted as having said “When it is evening, ye say, fair weather: for the heaven is red. And in the morning, foul weather today for the heaven is red and lowering.”
If the timing is right as a storm system approaches or departs, the saying actually does make sense but only in the mid latitudes where weather systems generally move from west to east. Because the sun rises in the east, approaching storm clouds will be highlighted red coming in from the west. At sunset in the west, departing storm clouds in the east would be highlight red. So, again, if the timing is right, then the saying absolutely makes sense.
The red color is made possible around sunrise and sunset because of the scattering of light through a much larger part of the lower atmosphere where suspended particles and aerosols are mostly found.