Less atmosphere favours the pellets more than the targets. Less air slows the pellets less so they are more destructive and also spreads the pellets less which gives a denser pattern and hence a higher likelihood of pellet strikes.
Any effect on the target is much reduced because they are set for the local conditions, that is, if the flight was hugely different, the trap would be adjusted to give the correct distance and height.
The differences are slight in shooting western clays compared to high humidity clays in the east. The average western shooter seems to have more trouble adapting to the higher humidity in the east for more reasons than just the percentages of humidity. Some shooters notice a slight delay in the time differences between shot and break when comparing those differences of east and west clays. How shooters determine lead also comes into play big time too!
Since the clays are aimed for distance and height from the trap house wouldn't that make the whole argument moot? Because a yard in humid conditions is a yard in dry conditions. And a foot at low elevation is the same as a foot at high elevation.