I don't wear religious head coverings and no one in my class year did consistently so I won't have the most accurate take on this. But the OMM faculty are very respectful of religious/modesty standards that people have so they work with students to find what'll work best for everyone (even if sometimes they're ignorant of the students' needs, if you talk to them they're usually very willing to listen and work with you).
The way the OMM dress code policy is written is that if you need to access someone's cranium/ears/upper neck/etc then it would be expected that you remove your head covering. But they also need to do whatever they can to give reasonable accommodations to your religion - including privacy barriers so only your OMM partner (and a professor if you guys need help figuring out the technique) can see you. I'm not sure if technically they'd be required to always pair you with a same-gender partner, or at least for sections where a head covering would need to be taken off, as there's also the reasoning that you'll need to treat different-gender people in clinic so it's important to get used to that sort of thing now.
In reality, the first time you work on someone's upper c-spine is second semester of first year, which gives you plenty of time to get to know your professors and talk to them about any concerns you have and how they can accommodate them. The dress code is also generally more relaxed than it is on paper - we're technically supposed to wear shorts and a sports bra (+ shirt) to every lab, but 80-90% of the class wears leggings/scrub pants/sweatpants even when we're doing leg and keep their shirt on even when doing thoracic spine. Some of us do this because of religious/personal modesty, but some of us also are just more comfortable dressing this way and I haven't heard of anyone getting spoken to about it since the start of my first semester, when they explained their concerns to our course director and they chilled out on always wearing shorts, for example. Our newer OMM faculty also feel that we should learn to assess and treat patients wearing clothes, since patient comfort is extremely important and most people would rather wear a shirt than be shirtless.
So tl;dr while the handbook makes it seem pretty hard-set, professors are people too and they understand that the educational benefit of having full access to a region we're treating doesn't outweigh the negative impacts of making people do things they're not comfortable with.
I think we do cranial OMM sometime next semester, so if I remember I'll try to update you then on how that goes/what the professors think about how to accommodate head coverings in that section.