I would leave it all white but change the door hardware or you could spray paint the handle a brushed silver;)

Do you know that you can purchase a rub on film that makes the windows obscure?
It seems to me that disguising the glass with paint could be dangerous. Someone could not realize that this is glass and accidentally put their hand through the thin glass.
Consider using the film, it will look elegant.

Another option that you have is to mount a small curtain rod across the top and bottom of the door and to put a curtain material from top to bottom. If you use a filmy material, you will be able to see that it is a glass door, but not be able to see through........

You can also put a spray on paint that looks like acid wash glass. But, another opinion of mine is, if you have white, red, why not add black on the glass? Those colors always look great together.