Would you have to accept a mental health referral for military sexual trauma?

No: I wouldn't say you have to. An ethical doctor would only accept referrals when they are available and capable of caring for the patients.

Depends who you tell: If you report military sexual trauma to your co or within the military, protocol may require a mental health eval to assess whether your trauma is affecting your line of duty. Another option is to seek care with a civilian doc, although they may not be expert in providing support tailored specifically for active duty serviceperson and/or dealing w/ military justice if you decide to press charges.

No: There is restricted and unrestricted reporting. The only way that a member of the military can be "directed" to a mental health evaluation is via a "command directed mental health evaluation". This can only be used in very limited situations. Even in that situation, the only legal requirement is to appear (not legally required to engage in interview). Military members do have rights.