Is it a moral contradiction to believe in the rights of animals while ignoring the rights of unborn human babies?

This is a loaded question. But to answer it, the stances you're alluding to (being pro-choice and being for protecting animals) are only hypocritical if the various reasons are conflicting. For instance, if you think abortion should not be illegal before 5 months, in part because the fetus cannot feel sense-pain (can only have unconscious impulse reactions) until the third trimester, and you think that the rules regulating slaughterhouses should be changed because the animals are made to feel physical pain - then no, those views are not contradictory. It depends on the individual philosophy of the person, and believe me, people have a lot of different reasons for believing what they do on this issue. I recommend to anyone that thinks being pro-choice means being anti-life or pro-death to find the smartest, most reasonable pro-choicer you can, and have a long and civil discussion with them.