D Dog, what you're encountering is not related to the other issues discussed in this thread. The other discussions relate to browser color management and/or color profiles on images.
Working with your site the trigger for the color shift is a specific rectangle that's ~12,000 pixels tall with a 75% opaque tiled image fill. It is the size of your browser area and behind everything. This particular object is hitting a limit in the 2014 and later versions of Muse that results in the fill transparency not being applied in Muse Design view. (The output is fine.) The lack of fill transparency results in the color shift in Design view.
This is a new limitation that was a side effect of the transition to a native app. We'll look at removing it, but it won't be trivial and thus won't be fixed easily or quickly.
That said, the identical visual design can be achieved more cheaply (in terms of total objects and page load performance) without using this semi-transparent rectangle at all.
Take the original tile image into Photoshop and composite it (adding the 75% opacity) with the blue background color into a new 100% opaque JPEG tile image and Save for Web as JPEG. It will provide the same visual effect and will likely be 1/10th the size of the original semi-transparent PNG.
Now delete the original rectangle and set the Browser fill to be the new tiled image. Since the very large object with fill transparency is gone, the color shift will be gone. There will also be fewer objects in the browser and less data to load at page load time.