Behavior considered deviant today may be socially acceptable after another generation or two, and normal within another generation after that. This has certainly been true over the course of the twentieth century, and may be no less true in the twenty-first.
At the turn of the twentieth century, premarital sex was considered deviant. However, that deviance carried a double standard. Single men were not really stigmatized if they had sex, especially if it was with "loose" women, though it may not have been something to mention in polite company. But if an unmarried woman had sex with a man, that brought shame. Even more shameful was having a child out of wedlock. In turn, men were expected not to have sex with "decent" women, or, if they did, to make it right by marrying them.
Today, it is common for men and women alike to have several sexual partners before finding someone they want to marry, and for this to be openly acknowledged. Remaining a virgin until marriage, or much beyond adolescence, has become the exception, not the rule. While there is still some stigma attached to having "too many" sexual partners, especially for women, it is also true that people may feel they have to make excuses if, past their mid to late teens, they are virgins or have little experience. Many single women have children and keep them, with no shame attached.
In a similar vein, until the 1960's, couples did not live together if they weren't married. In keeping with the strictures against premarital sex, it was deviant behavior for a single man and single woman to spend the night together. The 1960's and 70's saw more and more young couples move in together without getting married (although many did marry later on). By the 80's, many middle aged and older couples were doing the same. Nowadays, it is so common for couples to live together before marriage that cohabitation could be said to be the new norm.
A hundred years ago, it was deviant for women to wear pants. A woman who wore them was cross dressing, and a woman who wore them in public could be arrested for indecency. Now, women may wear pants in all social situations, even as part of formal wear. Pants are part of every feminine wardrobe, sometimes to the exclusion of skirts. In contrast, men are still considered to be cross dressing if they wear skirts, and while cross dressing may have gained social acceptability in some circles, it is not completely free of the label of deviance.
Probably, nothing has changed from deviant to acceptable in so short a time as homosexuality. While homosexuality is still considered deviant by some, it is accepted enough that some countries and states have begun to legally recognize same sex marriage. It is also more and more widely accepted that homosexuality is a natural orientation, not a choice, and not anything unnatural in and of itself. Even many who do not believe in same sex marriage do believe that same sex couples should be allowed legally recognized partnerships of some kind.
While not as stigmatized as sexual deviance, left handedness was considered deviant enough in generations past that left handed children were often forced to switch to their right hands, and punished for using their left. Nowadays, every kindergarten classroom has a few pairs of left handed scissors, and left handed children are not asked to change. It is still a right handed world in many ways, but left handers are considered simply another kind of normal.
Considering how rapidly what was deviant in the past has become acceptable, it is intriguing to think what the great-grandchildren of today's young adults will find acceptable that is deviant to us. If change continues at such a fast pace, the social world of the late twenty-first century will be very different from ours.