Wow, some people are a**holes when it comes to personal body matters. I seriously fail to see why anyone should allow a doctor to perform an intimate exam on them that is completely unnecessary. So what, you guys want to scar a woman for life?
Anyway, that's the main reason I answered, but unfortunately, it is the Army and they operate on the same procedures everywhere in the US. I tend to think that if you refuse to operate by their standards, they have the right to refuse you. I'd go higher than your recruiter and talk to someone who will actually be where you will be shipped off too, as you said, your recruiter may be biased. In any case, I seriously doubt anyone, even in the Army, can force you to undergo a medical procedure that isn't even needed. So even if you went and they decided you either do it or leave the army, you could always still leave.
Of course, I don't know much about the army, but I was just appalled to see people so blatantly undermining your beliefs. Good luck! <3