What is David Lynch's obsession with stages, red curtains, and female singers?

With regards to the curtains:

The red curtain is a recurring symbol in Lynch’s works, having its first appearance in Blue Velvet. He has expressed his fondness of a particular moment – the moment when you are sitting in a movie theatre and the lights go out, the curtains open, the movie begins. And it takes you to another world. This particular moment is what has inspired Lynch to use this symbol more than once.

The red curtain acts as a medium, a Demiurge of sorts between the real, material world and the dream world. In Twin Peaks, the Red Room, with red curtain walls is the place where spirits go on their way to perfection, a place halfway between both worlds where anything can happen and there is no problem with time.

This Tumblr contains a selection of (unfortunately unsourced) quotes:

“Curtains are both hiding and revealing. Sometimes it’s so beautiful that they’re hiding, it gets your imagination going. But in the theatre, when the curtains open, you have this fantastic euphoria, that you’re going to see something new, something will be revealed.”

That same quote is also posted on this page.

In this interview Lynch claims not to know the origins of his fascination:

'I don't know where it came from, but I love curtains. There is something so incredibly cosmically magical about curtains opening and revealing a new world. It resonates on a deep level with people.'

Here's an interpretation of the theme by Matt Pearson:

The world beyond the radiator is given a very theatrical setting; the stage, the spotlight and the surrounding curtains. This idea of performance recurs also; it is a stage on which the Elephant man is displayed, where Dorothy sings in Blue Velvet, and Julee Cruise in Twin Peaks. When Sailor dances in Wild At Heart it is very exaggerated performance, as is Lil's dance in Twin Peaks: Fire Walk With Me. The curtains are a motif: the title sequence of Blue Velvet, the decor in the Black Lodge (the floor design mimicking that of Henry's apartment block) and the academians view of the Elephant man; silhouetted through curtains. Nadine, in Twin Peaks, is obsessed with the smooth running of her drapes. The curtains also link us to night-time, when most of Lynch's action is set, especially in Eraserhead and Blue Velvet. Spotlights are used to highlight certain elements of mise-en-scene, with unnatural pools of light featuring strongly, especially in the black and white films. These pools of light are often cast by standard lamps which are compulsory furniture in Lynch's world.