Answer: almost always, yes
Red food coloring used in food products is currently almost always vegan. Years ago, red food coloring was created with carmine (check our carmine post, not vegan), carminic acid or cochineal. Today, most food grade products with red dye use Red #40, which is derived from coal (gross, but vegan). So double check those red food coloring jars, but chances are, vegan.