I am hoping that a member of the military chaplaincy or someone else with relevant experience can clarify something for me: I understand that homosexuality, whether as an actual physical act, an identity, or a lifestyle, violates the religious beliefs of many chaplains. From reading letters and articles by and about this issue, it seems that a fear of the chaplaincy is that members will be forced to deal with those who openly profess this identity/lifestyle/activity and will not be free to express their religious conviction that it is sinful, or immoral, or harmful, and may even find themselves in a position where their job requires them to be supportive of homosexual soldiers in a way that directly contradicts their deeply help religious belief. What I am trying to understand is how this is significantly more challenging than ministering to those who are simply not of the same religion. As an example, I am Jewish. I explicitly deny that Jesus was in any way more or less divine than any other person alive or dead, and any number of other core beliefs of most Christian sects. There are many people in the army today who hold similar views, for many reasons, but let's stick with the Jewish example for ease of reference. I hope that if a Jewish chaplain was not available, and a Jewish soldier was in need of ministerial guidance, I cannot believe that the current military standards would condone a Christian chaplain telling that soldier to seek solace by accepting Jesus into his heart. Similarly, the issue of teaching straight from the Bible has been raised, as if the military does not already openly condone many religious beliefs that the Christian Bible declares immoral.
Since I have not had the privilege of serving in the military (not for lack of trying, but I was told my medical condition is a non-starter), I do not have first hand experience with this, and it is possible I'm missing a point here. Can anyone explain to me what is done right now to deal with the above situations, and what is preventing that policy from being extended to similar situations with homosexual soldiers?

From the Christian's perspective, it is one thing to persuade a non-believer to your faith, and another to affirm immoral sexual behavior. For the Christian to persuade you that Jesus was the Messiah and foster your conversion to Christ is simply the presentation of a truth claim, and there is no moral impact on the Christian if you reject his position and his faith. But let's add in three relevant components: You are in the military, you are a practicing homosexual, and the military has officially affirmed homosexual behavior. The Christian's ability to present truth claims in that context is now limited by regulation–whereas he could safely say to an adulterer that that form of sexual behavior damages his humanity and is an indication that he needs a relationship with Jesus Christ, he can't say that to you regarding homsoexual behavior without running afoul of the inevitable nondiscrimination claims. Bear in mind that the consistent evidence to date is that the homosexual side will demand absolute affirmation and have zero tolerance for any moral dissent–so there will be systematic suppression of Christian truth claims. That said, you are correct that a Chaplain would have an obligation to give you moral/ethical counseling regardless of whether there is a “match” between your faith and his, and that that would not be the proper place to proselytize, and that is not an improper burden on the Chaplain. But under the proposed system, he wouldn't even be able to use Christian beliefs as an example in moral counseling on a matter involving homosexual behavior–rather he'd have to affirm that the behavior is OK even when he believes that there is an objective truth saying it isn't. That puts him in a clear conflict of conscience.