"Red sky at night shepherd's delight; red sky in the morning shepherd's warning”, is there truth behind the popular phrase?

The colours we see at sunrise/sunset are because of sunlight being scattered as it passes through the atmosphere and ricocheted off water vapour, aerosols, and dust particles in the atmosphere.

It is the amount of water vapour and particles in the atmosphere which give the indication of upcoming weather conditions based on the colours we see.

In the mid-latitudes, weather moves from west to east. So, when a storm exits, stable weather arrives from the west. The sun, which sets in the west, then illuminates the departing clouds with hues of orange, yellow, and red.

This is what makes the first half of the saying make sense scientifically: "red skies at night, shepherd's delight."

However, should you see a red sky in the morning, the sun, which rises in the east, is illuminating the clouds of an incoming weather system and rain from the west. This is why the phrase ends with "red skies in the morning, shepherd's warning".