Transgender Bathroom Debate

I was having a conversation with one of my best friends about transgender bathroom yesterday, and she is against them. I have no problem with different opinions and views, but I feel that the justification for their beliefs should be good or at least not ignorant. Our conversation quickly turned into a debate, and she began telling me how she thinks that "you don't know what could happen if you let these people use the same bathroom" She then began to talk about how "if you give these people the right to use our bathrooms, the next thing they'll do is rape people, hold office, corrupt the next generations" It was so ignorant and a pretty shitty reason. I had an hour long debate with her over it. And towards the end, she finally snapped at me and said "Does it even matter? It's just a bathroom. People just go there to pee" And I stopped and said, "Exactly. Why should it matter then?" And she stopped and realized that it shouldn't matter. Towards the end, I felt pretty satisfied, but it was interesting to see how her reasoning unfolded and how she realized how ignorant she was being and how her views had no basis.