Transgenders in the military?

I recently got into a discussion with a friend of mine who called me a bigot for my position on accepting transgenders into the military. We're both army brats, so we both have parents and other close ties to the military. I said that transgenders should be allowed, but that they should serve as the physical gender they are, regardless of self-identification, as the military should not redirect resources from vital operations to make a person who has not undergone surgery feel more comfortable (example: allowing a physical woman who identifies as a man to be allowed to serve infantry, which is not an option for cis-gendered women) . I said once they had undergone the surgery, it would be totally fair for the person in question to request they be reassigned gender quarters etc. I also said that the military should not be required to pay for the procedure, as again, they need the money for other operations and it is not their responsibility. I would say the same to those with disabilities. My logic is, is that the military is not the civilian world; it is a service and a job and it does not exist to make sacrifices to serve you, you make sacrifices to serve IT. My friend (whom identifies as the other gender) got angry with me and called me a bigot, so I'm kind of concerned now. Is my position really that unreasonable/ignorant?