I think there's a difference between wanting to behead them and not allowing them to be elligible for office. Both are absolutely wrong, but by orders of magnitude differently wrong.
Yes, but the difference is not in what each religion
says, but in what its followers
currently interpret it to mean.
That is, in scriptural terms, both Christianity and Islam say surprisingly similar things about homosexuality. The difference in how the majority of Muslims, and the majority of Christians, feel about how those scriptural dictates should be implemented, however, is
very different (for the most part...there are still
far too many American evangelicals who would be happy as clams if stoning were implemented as a punishment for gays and lesbians). Since that difference is rooted in cultural and historical issues, and not scriptural and theological issues, though, there is an opportunity (if not a mandate) for a reconciliation and moderation to occur in Islam, just as it has in mainstream Christianity.
That is, the problem is
not Islam (as people like the OP would have it), but with a
particular modern and popular version of Islam. And while that may still be a particularly large obstacle to overcome, it's still a
hell of a lot easier to overcome than the alternative.
It's not a forgone eventuality, but it's at least a
possible one.