The chain of command is very handy for seeking guidance on issues like this, and you will be seeking information from those most likely to know current policy and acceptable practice for ROTC for your service. It won’t be a new issue. You will also then be prepared to counsel those junior to you when the issue arises again, knowing your information comes from official sources and not anonymous Internet forums, which may or may not be accurate or current.
You can also practice your JO skills by researching applicable ROTC uniform wear regs online yourself, and if something is unclear, follow up with COC. Never delegate tasks upward that you have not first attempted yourself.
Here’s some classic pro reading, if you haven’t encountered it yet:
This memorandum on completed staff work, first issued during World War II, has become the widely accepted definition of what effective staff members do.
govleaders.org
Finally, good for you that you have heard something about uniforms and their relation to political expression, and that you are pausing thoughtfully to explore the issue and ensure you are doing the right thing. Well done.
My two cents and IMHO is it’s a college class you have to attend, not a political rally, you’re not using your uniform to imply DOD endorsement of a candidate or cause, you have no agenda except to complete the requirements of the course. Asking about this with the COC will demonstrate you are starting to think like a JO. Win-win.