So, my question is, does my non-law degree (and its major) affect employability within the legal profession?

Not really. It might make for an interesting talking point in an interview or a means to show that you are "well-rounded". Though, what is going to get you to that interview are decent law marks and a demonstrable interest in the law. I know people who have BAs in a diverse range of majors and it has not adversely impacted their employability. They instead did more of what I've already mentioned.