When I first showed up to USMC OCS, we got our supply issue – which we paid for, oorah. In this supply issue were a couple of jock straps, and tighty whities. Being a boxer man myself, I thought well sNit, they can’t expect me to wear these things. What I found later is that all we would wear were these little green PT shorts, which had built in underwear (some wore jockstraps/whitetights underneath, I didn't). We wore these (still do) for everything, including PT. These are nylon shorts that look like the old school jogger shorts from some decades ago with the slit up the sides all the way to the waistband. They offer a little support for your junk, but still allow for good circulation. I mention this because my Navy friends said that they had the same shorts as me in boot camp except that they were blue. (Note, this was boot camp, I don’t know about OCS)
I don’t know if they had rules or not, but since you will be dealing with Marine Drill Instructors, I can say that they won’t be asking you to remove your shorts for a jock strap check. If you wear something that they can notice, like the “joe boxer” waistband sticking out, expect an immediate thrashing. The bottom line, is don’t draw attention to yourself, be conservative in your choice of underwear, and if somehow you are challenged as to your choice of undergarments, Marines like confidence convince them as to why you should not be allowed to wear a jock strap. For example if you were to sound off “This candidate’s hometown doctor told him that because he was batting a low score if he were to wear a jock strap, it could make him sterile!” Not a lot of people have the confidence to sound off like that to a 210lb Drill Instructor, but I can assure you that is part of the game that they enjoy. Good Luck.