You might be surprised at her reaction. If she is anything like me, she would appreciate the differences being brought up to her. Pretty sure, given all her other dealings with you, that she would recognize the value to her of that information.
I understand that it can be very hard to trust that. But trust is never 100%. There will always be an occasion in your relationship when you will become aware of her lack of understanding of a particular form of privilege.
But if she has been as good of a friend as you say she has been up to this point, she will welcome being informed about the reasons for your differences in reaction to the same situation. As a white woman who goes out of her way to pay attention to her privileges in particular situations, I welcome any and all information that educates me more than I have already educated myself.
And I would be heartbroken to not be trusted with being made aware of how I may have been unconscious of my privilege, and to have hurt and become mistrusted by a friend like you as the result of my lack of consciousness.
I urge you to talk about your feelings regarding that experience.
One non-threatening way of beginning a helpful discussion of it might be to start with...
"You remember when you insisted you would be safe walking home after dark? My shocked reaction was based on how much I have to fear in such a situation myself. It made me very much aware of your unconscious privilege, and for me it meant that a rather large chasm had opened in our friendship."
You don't have to accuse her of anything. Just stick with how you felt about what happened.
I can guarantee you 99.999999% that she will be apologetic and will thank you for helping her to become more aware of her privilege.
In fact, I rather suspect that she thought about that afterwards and may be trying to figure out how to bring that into a conversation with you.
Please give it a try. I guarantee you 100% that you will not lose your friendship with her by the mere fact of your wanting to talk about it.
That's what real friends do with each other, regardless of the subject matter.