The bible is clearly not a single book, it's a collection of writings by different authors hundreds of years apart. Of course it's contradictory. Also, not everything in there is equal in terms of importance. The 10 commandments are pretty high up there in terms of importance, but even they were supplanted by the teachings of Jesus (which can be summarized as "love one another").
Bigots usually find their justification in Leviticus, which is a minor book explaining rules for the Hebrew society in like 1000 BC. That's the only place where homosexuality is mentioned, for example. But then, it also says women in their period have to sleep in a separate tent.
Anyway, if you research it properly, you'll see that stuff like hating gays is actually a worse sin than being gay. I haven't researched abortion specifically, but even if you consider it a sin, all the hate around it is a worse sin anyway. Jesus said that heaven is happier with a sinner who repents than with someone who never sinned anyway.
I'm not really religious, but I was raised in a religious family that actually follows that philosophy (love one another).