its actually on the side, so you can see it from the street. But I think it looks strange having a casement there anyway when it is open. its just sticking out of the side of the house on an otherwise blank two story wall.

If it's the only window on the wall, you can do what you want with it.

But you can also address the privacy issue with a window treatment if you want to keep them all the same.

I don't think it's a problem at all. An alternative would be a large window that doesn't open paired with a small awning window above or below it. The windows can have rain glass or some other privacy glass so that you don't have to add window treatments for privacy. I would use privacy glass even if you use a double-hung window so that you can still get light without having to worry about privacy.

Totally fine. Good idea, in fact.

my main bathroom window is right next to the entry, so someone standing on the front porch can look right in to where the toilet is. I have mostly casement windows on that side of the house, but when I replaced the windows, I put in a double hung and factory ordered the bottom half with obscure glass. It's perfect. I can still see the sky and no one can see in at all.