With only a skimming of the thread: Is it moral? I don't know if it's moral or not, but it is definitely a question that can and should be asked. In my view, it's not necessarily due to doctrinal issues within the realm of Christian teaching though, it's a semantic issue on a broader level. A lot of groups that somehow use the word Christian may or may not be Christian in actuality. A lot of redefining goes on with certain words, and Christian seems to be one of them. There's only so far you can go before you're completely redefining the word and it becomes meaningless.
The case of Christianity and Buddhism is such an example. On their own, Buddhism and Christianity are distinct belief systems. Despite certain similarities in teaching, the core doctrines of what makes up the belief systems are completely different. Some people sort of mix and match them a bit and they can be sort of a "Buddhist Christian," but depending on how this mixing goes on they aren't really fully adhering to one or the other. They may be a Christian with elements of Buddhist practice, or a Buddhist with elements of Christian practice. If they are truly somewhere in the middle and have completely blended the spiritual beliefs of both (i.e. Jesus was a form of the Buddha or something), then they really have a new religion on their hands.
The most basic definition that qualifies a belief system as "Christian" is a belief in Jesus, that he died on the cross for the sins of mankind. This definition is extremely broad, and really isn't sufficient. Christianity should also entail acceptance of more propositions such as acceptance of monotheism derived from Jewish tradition, for example. Keeping within the realm distinct to Christian tradition (which is itself derived from Jewish tradition) is what keeps the "Christianness" in something, I think.
Because of this view I tend to put groups that some perceive as "non-Christian" (such as LDS, Jehovah's Witnesses, etc) into the "Christian" category. However, I do make a further distinction between orthodox and unorthodox for those groups. But, that's a separate issue entirely.
What qualifies as "Christian tradition" is also a bit vague. It can only get so exact, but developments contained within Christianity itself or developments that are not otherwise heavily syncretistic are what qualify, in my mind. This includes innovations on already-existing forms of Christianity such as the various strains of Protestantism, as well as certain movements like the LDS. Neither of those movements are direct syncretistic fusions of another religion into Christianity. While the movements may contain ideals specific to their founders, those ideas are still innovations on the then-current belief.
This allows for ideas of other philosophies or beliefs systems to influence Christianity, but prohibits the direct lifting of elements from other religions. It allows for a broad definition of what constitutes Christianity, and includes almost every group that self-identifies as Christian, but it's not so vague that any religion can go calling itself Christian and not have basis in the historical religion at all.
As for the topic of gays being Christian, the definition I've made for myself here would include them. There isn't any reason they should be excluded from self-identifying as Christian. They should be rightly entitled to using the word to identify themselves. However, within the realm of Christianity, there is still the concept of sin, as well as a historical teaching that homosexuality is sinful. The umbrella of Christendom rightly still includes those who think that homosexuality is a sin, and their arguments against it, just as it includes those who support homosexuality and don't think it's a sin.
