That is ridiculous. You look absolutely beautiful and this is you, this isn't a costume or a performance. This is who you are. If she can't respect that, and if your friend isn't willing to stand up for you, then I would seriously reassess those people being in your life.

Don't stifle yourself for others dignity. Theres nothing to be ashamed of being see with a transgender person. If her friends care that much, then they're garbage friends. And if it matters that much to her that she would ask you to do that, then she doesn't understand or respect you in any way.

This might seem small to you, or like it might be easier to just pass it over and go on about your day but you do not deserve that. Its okay to set boundaries with people and other people telling you how you should be is absolutely something to make a boundary about. Don't let other people control you. You deserve to be yourself and have your friends accept support and encourage you to be yourself.