We all know that toothpaste helps promote oral hygiene. It helps remove dental plaque from teeth and it suppresses halitosis while preventing tooth decay and gum disease because of ingredients like fluoride. It's packed with anti-bacterial agents like Triclosan or zinc chloride which help prevent gingivitis while reducing tartar and helping to freshen breath. When advertised, it's said to whiten your teeth or make your breath smell better. It does all those things with a flavouring that makes it palatable for most people. Toothpaste also has to be attractive to the eye. You wouldn't use a green gungy-looking toothpaste or anything that might remind you of vomit or bile, would you? Toothpaste that's marketed as "whitening" your teeth is normally white. If a paste is marketed as being natural, it's often mint green. So the colour is important even though it's scientifically the least important elements of toothpaste.
As toothpaste is supposed to provide multiple benefits like building stronger teeth, keeping your breath fresh or whiten your teeth, some toothpaste manufacturers like to represent the multiple benefits of toothpaste. The most obvious brand is Aquafresh which is a mixture of three colours – red, white and blue. These colours represent different things that the manufacturer calls "Triple Protection". The white illustrates decay prevention, the blue is for freshness and the red represents plaque prevention. Of course, you can't squeeze out the blue part and expect to just benefit from freshness. This is just a marketing message that's powerfully conveyed by the three equal stripes.
The message carried by the three colours is so powerful that consumer healthcare product maker GlaxoSmithKline has trademarked it. They went to court to protect their brand when major rivals Colgate attempted to market as toothpaste with blue, white and green stripes and use the "triple protection" tagline in their advertising. The case was settled out of court but it illustrates just how important the three colours are in a very competitive marketplace.