Is it true that the stripes on the toothpaste mean something?

This is technical markup. Photo tags are usually used of two types:
- horizontal - for precise cutting of the laminate in height (when printing on a roll laminate)
- vertical - for precise positioning when soldering the tip of the tube (so that the solder is parallel to the image and the text part , not at an angle or perpendicular)

This mark is read by the light beam, and for the sensor to recognize it, the color must contrast as much as possible with the background color. So, for a white / light tube, the most contrasting color will be dark / black, and for a dark tube, on the contrary, white / light.

The color of the photo tag is selected from those colors that are used in the packaging design of a particular toothpaste or cream ... That is, if the design of a light tube contains black and green / blue colors, then, more likely, black will be used for the photo tag. But, green on a white background, like blue, is also quite relevant.

No. The mark on the toothpaste is needed during production, the photocell sees it and the machine "understands" where to cut the tape and how to roll it up to make a finished tube.

The color of the label is usually chosen for practical reasons - the most contrasting background.