Does red lipstick have bug guts in it?

No. Red lipstick has a colorant called carmine in it. They make it by boiling the shells of an insect called the cochineal in a sodium carbonate solution to extract the carminic acid (which the bugs make to deter predators), then adding alum to turn the solution red. After they dry it out, there's your pigment.

So...it's not bug guts, it's a chemical derived from bugs.