That red thing is unidentifiable as anything but sperm. If they were going for a lipstick reference, why not the kiss print? The kiss would be generic, but this "smear" isn't complete enough to suggest that reference. I kinda thought maybe it was a wig at first, but did Santino wear a long, flowing, Wendy's-red wig? As a designer myself, I simply don't understand what logo/branding design has come to on Broadway recently.
I'm kinda surprised they don't play into the masculine/feminine duality, that would be a much better concept for a design and give a much better inkling of the show's plot.