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Christianity does, Leviticus it states " "And if a man lie with mankind, as with womankind, both of them have committed abomination: they shall surely be put to death; their blood shall be upon them." now we do not take that to its literal meaning in christianity do we, why should we expect Muslims to within their religion.
Corinthians states "But I would have you know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God. " which is pretty pervasive in meaning. there are many more. Again its about interpretation. With a more modern view of each religion this is apparent.
You're quoting two inaccurate translations from the Jewish section of the Christian bible, which can be ignored by Christians in a way consistent with their own religion(*). Your point is therefore much weaker than it might at first seem.
This, for example, is the literal meaning of the thing forbidden verse you quote from Leviticus:
And with a man you shall not lay lyings of a woman.
It isn't an abomination, either. That translation is also wrong. It does carry the death penalty though, like so many other things in the OT. It's also in a section about other religions, which has led some people to translate it as forbidding the ritual sex that occured in some temples in some religions in the early days of Judaism (bearing in mind that this passage is Jewish, not Christian). Others translate it as forbidding men to have sex with each other in a woman's bed, which isn't as silly as it sounds today. There's a lot in the OT about what can be done where.
You'd be quite hard pressed nowadays to find Christians advocating death for homosexual men. There's the Westboro Baptist Church, but they're so vile that they've been formally disowned by other churches.
It's not the same situation.
* There is a lot of scope for Christian debate on what to do with the essentially Jewish Old Testament, but my point is that it is internally consistent within Christianity to consider it superseded by the New Testament.