Perception is reality. The perception of what society deems as moral is in fact morality. Relaxing the perception of what society deems as moral is in fact relaxing morality.
I don't agree. A major myth of the components of society is a shared (or common) morality. Although on the surface, I admit your assessment of the definition of morality is accurate, it just simply isn't true. Morality is, as always has been, completely individual in nature...and practice. The social concepts of morality rarely (if ever) change based on a small amount of people acting in contrast to that social moral ideology. The change occurs when large amount of individuals act in contrast to that morality. This occurs because large amounts of people have been acting in contrast to that morality for what is usually a long time prior to the change.
Take the perceived changes in American sexual morality. Whether you are looking at female promiscuity or homosexuality, these changes didn't begin in the 60's and come to the current state. Homosexuality and female promiscuity were alive and well long before the public perception changed. Although PERCEPTION of the acts might have been seen as immoral by "society", the morality of these acts were not questioned by most of those acting.
In regards to morality, liberalism seeks to relax the perception of morality from applying traditional standards and allow the social perception to incorporate differences in individual spiritual and sexual ideology. Though there is still morality. It's still immoral for a homosexual or a promiscuous female to cheat against the will of a partner (or spouse). The relaxation only applies to the traditional standards based mostly in religious ideology.
It's just ridiculous to think of morality as anything more than an individual's relationship to the world around them, and how their personal views of life, living, spirituality, ethics, and justice are applied to their actions. A social perception of morality? It only leads people to "act" like they want to be perceived when people are watching....behind closed doors, it is (and always has been) an individual concept.