We're always told that the new testament should be followed and overrules the old testament, which is basically kept as a bit of background reading, which is why we are apparently not supposed to keep slaves or kill everyone from a different village. But somehow no-one ever manages to explain why we are still supposed to believe in creation or hate gays, when that is all from the old testament as well.
That's such a simple one I'm surprised people are asking it. The Old Testament is not a monolithic text. There are numerous components, and distinctions between them. The story of Creation is part of the history, and as such, not subject to modification. It simple describes what happened (albeit in more metaphorical language than the fundies like to believe). The commands given to the Hebrews regarding purging the various pagan tribes in the land were part of the Old Covanent, the Covanent of Holiness; and were for a specific place and time. There is no indication that it was ever intended as anything more than that.
The important and controversial part is the Halachah, the Law. But even that is not monolithic. There are multiple components to the Law as well. The Aseret ha-Dvarîm, also known as the Ten Commandments, is the foundation for all the Law. This could be considered the most important out of all the Law, and isn't changed by the New Covanent.
Then there is the "ceremonial law" regarding religious observations, social laws for jurisprudence and mediating disputes, and so on. These are collected and elaborated upon in the Talmud. Some of the ceremonial, such as the kosher laws, had purposes beyond the mere symbolic; but many were simply that.
The Covanent described in the New Testament superceded the ceremonial laws, and decanted the underlying principle of the entirety of all Laws down into two fundamental laws - love G-d with all your being, and love everyone else as much as yourself. "From these proceed all the Law and the Prophets." It did not abolish the Law, it clarified it and it's true purpose. The rest is merely elaboration and explanation of specifics.
And the new, there are versed in Romans which condemn homosexuality, and some verses of Corinthians which can be interpreted that way. Mind you Corinthians also contains passages which say than men having long hair is ungodly, which make the standard image of Jesus and the Turin shroud even more suspect than they already where.
Actually, the verse refers to a man having his hair "as a woman's". It did not specify length, which was similar for men and women, except insofar as men shaved their heads for certain religious ceremonies. It's referring more to the adornments, perfumes, and styles common to women of the time. It is in a similar context to those condeming a man wearing women's clothing, and is generally seen as a proscription against transvestism/transgenderism in a time and culture (Roman) where TV/TG prostitutes were commonplace.
