I have an etoupe Birkin with rose tyrian interior. My favorite way to carry it is with the straps slightly undone, and as you can see in my picture the color is very obvious. I only carry it that way if it coordinates with my outifit. Otherwise, I carry it with the straps latched and the flap tucked in. Small slivers of the inside color can be seen, but only from certain angles. It's not obvious head on and it isn't obvious enough for it to clash with what I'm wearing. Hope this helps!
Thank you so much for the illustration!! That is soooo super helpful to me!!! I love your bag, btw!!!