I agree with Moray, Mental Magpie, etc.
If I were in your situation, I would not make a point to go around telling people, in part because it would be very hard for the listener to determine the truth of the situation, especially if they're friends with you and Carrie. They won't want to believe their friend is a bigot, nor would they want to think you wouldn't tell the truth, or would blow something out of proportion. So, it'll create she-said/she-said drama and people taking sides.
However. Sometimes possibly creating drama is worth it. And in this case, I would be truthful if asked. It's something that is very important to you, and Carrie's behavior wasn't just discomfort or awkwardness. She said 'freak' which means it wasn't that she was frightened or thought an actual man had walked into the women's washroom. So, if someone I considered a good friend asked me why our friendship is cooled I would say something like 'she yelled at someone she thought was trans in a washroom and now I can't see her the same way again'. Don't ask or expect the other person to do anything about Carrie on their own, expect that they might stay friends with both of you. But, I think you have the right to be honest if you make that choice.