The food itself isn’t necessarily red, but there are certain nutrients that will make the yolk redder. Factory farms can adjust their feed to tailor the yolk color for different markets. pasture raised eggs will very in color seasonally and regionally with what food is available to them.

Kenji did a blind taste testing once with eggs of different colored yolks. The yolk color is based on the feed of the chicken, but from his testing, people didn't notice a taste difference but did prefer the more orange colored yolk when they could see the egg.