Natural Folding Drape Curtains
With the same materials used on wovenwoods, natural folding drape curtains are a version that moves left to right. Makes an excellent window treatment for a sliding glass door.
Vertical Shade Blinds
I know vertical blinds have a bad reputation but if used properly they can last a long time. Verticals, like horizontal shades, offer all those light and privacy control options you are looking for. Like everything else there are a ton of fabrics and colors to choose from and you will not spend a fortune.
Sliding Panel Curtain Shades
Panel curtain shades slide on a track and overlap each other as it opens. You can match your solar shade fabrics and keep your view or pick a light filtering fabric for more privacy.
There is nothing wrong with putting a roller shade on a slider if it works for your situation. I have used them many times. You can see the blackout roller shade I put on a slider in the image above.
Vertical Cellular Shades
Both Graber and Norman offer vertical sliding cellular shades for sliding window covers. Same color options available we are just moving it left to right instead of up and down. A great solution for any sliding glass door.