If my girlfriend is on the birth control pill, and takes it religiously every day, is it really necessary for me to wear a condom? Or is she just being paranoid because you hear stories about people still getting pregnant while on the pi

No birth control method claims to be 100% guaranteed. Your girlfriend clearly does not want to fall pregnant and is being responsible rather than paranoid - why should she take total responsibility for your contraception. Also consider that condoms will protect you both from STD's - dependent on how long you have been together etc maybe she is also concerned about this?

Maybe she wants to be extra safe. I saw someone compare taking birth control pills and using a condom to using an umbrella and a raincoat in the rain. That may have even been on here. Try thinking about it that way instead.

Either she's paranoid or she doesn't trust you, as in STIs