How can Christians follow one part of the bible yet totally disregard other parts?

Oh it's really easy - it's called "double think" (Wiki it). But seriously you're thinking about it all wrong. There's no logic involved with religion - it's just an excuse for someone's prejudice and hate. Whatever is convenient for the believer is what they believe in. Some complete will use the bible to justify their hate because "the bible says so" but when you confront them with something like what you mention above they'll just be like "nah, nah, that's just outdated stuff that you don't have to follow". Idiots.