The mountains are affected by the atmosphere because they are in the distance. It's a question of scale. There are two ways you can try to reduce the atmospheric affect on the distant mountains with minimal change to the sky:
1) Reduce the scale of your terrain (this might be difficult)
or
2) Reduce atmosphere densities (bluesky density, haze density), and increase the scale of the atmosphere to compensate so that the sky remains similar. You can increase the scale of the atmosphere by increasing bluesky exp height and haze exp height.
Bluesky exp height and haze exp height control the rate of falloff with altitude. Doubling these values would result in doubling the density of sky if you were looking up at the zenith from a camera altitude of 0, so it's an effective way of separating the appearance of the sky from the appearance atmospheric effects on local features like mountains.
As a quick experiment try, multiplying your bluesky density and haze density values by 0.25 and multiplying your bluesky exp height and haze exp height values by 4. The sky should look reasonably similar to your original render as long as your camera altitude is not too far from 0.
(The 'blue sky' component and the 'haze' component both affect distant objects, just like they affect the black of space to give the sky colour.)
Matt