Morality is an entirely subjective concept, and should not be used as a weaponry. The West has developed for many years and have ascended through times from ancient religious principles to the notion of modern basic human rights. However, I'd like to address that by saying the notion of "basic human rights" isn't universal, it's a standard of the West. The East doesn't do it perfect, but neither does the West. This whole affair is an eventual reality that happened to spark in the era of our existence, due to an inherent ideological difference. This is no right or wrong here, only a side to take, but to attack the opposite side of being immoral based on one's own judgmental system is simply not constructive.
As humans, the least we can do is to be aware of the situations and stay open minded and be respectful of each other, and our differences. That's how we can together evolve to a possibly harmonious future, at least to the extent of the upper-bound of humanity. There isn't a single standard of morality, and a heavy indulgence on one single side will eventually run yourself into a corner of being seen as practicing double standard.
Let's call it for what it is, a challenger to the current supremacy and that's that. Conflicts arising due to ideological differences is hard to resolve, but to only address the other party as immoral is an extremely short-sighted strategy to addressing any differences between the two. It's a greatly sad affair to see the propaganda machine on both ends flexing their muscle. Either the challenger will be defeated and we accept a new reality, or the existing supremacy loses and accept itself as a second. Bringing in a self-righteous morality to the mix is only going to incur permanent damage to humanity as a whole by prolonging the battle between ideals.