I think the since Liza Minnelli is an icon among drag queens. She was basically insulting ruby telling her she dresses like one.
Granny says Red started transforming when she was 12 or 13, right? That is a normal age when the menstrual cycle starts. There could be that connection. Or it’s just because it’s the supposed start of puberty.
I think Red starting her transformation at the age of puberty is a totally a connection to her sexuality and her wolf.
Regarding her two different selves
Red/ Ruby reminds me of this quote from Dr. Clarissa Pinkola Estés, who wrote “Women who run with the Wolves”:
A healthy woman is much like a wolf ~ robust, inventive, loyal, fierce.
Yet separation from her wildish nature causes a woman to become meager, ghostly, anxious about leaping, fearful to create new life.
This describes Red and Ruby both, it just manifests itself in two different ways.