The Camera > Standard Views are inexorably tied to the inalterable world axes.
However, you can set the drawing axes any way you wish.
Then, you can align the camera to the blue axis with the view rotated such that red is horizontal onscreen.
Use the Axes tool.
• Set the red axis along the edge you wish to appear horizontal onscreen; blue pointing up as usual.
• Then, right context click on any axis > Align View
Result:
The camera moves to the blue axis pointing at the drawing axes origin.
And…
The camera rotates such that red is horizontal onscreen.
Like Box says, create a Scene to return to those camera/axes settings when needed.