Here is the NFHS rule:
3-2-5 . . . Headwear (caps, visors, headbands, ribbons, etc.) may be mixed. If worn, they must be white, black, beige or school colors (the colors are not required to be the same for team members). The logo may be any color. Flat items, no longer than 2 inches, used to control the hair, such as bobby pins, barrettes and hair clips, are permitted. Plastic visors, bandannas and hair-beads are prohibited.
I honestly can't see making a player take off this hat, but if you really get technical...Rules state that the uniform may have only one manufacturer's logo. If their jerseys are, say, Under Armour, and the cap has a Nike emblem, by the strictest reading of the rules the hat would have to go.