Complicating matters, our sense of what’s ideal can be fickle. Children, who by age 3 have ideas about what is normal behavior,  are prone to seeing an instance of a random behavior—someone taking items out of a bag in a certain way, say—as exemplifying a norm, even without any prompting.  Among adults, too, conventions can emerge with surprising speed.A University of Pennsylvania study asked members of a social network to look at images of adults and name them. After each participant shared his or her suggested name with just a few others in the group, the entire network quickly reached consensus.  This helps explain how names that were uncommon 20 years ago, like Aiden, can become, well, normal.
Norms can also shift quickly on more disturbing matters. In one study, a group of women was shown a movie that presented stalking as romantic. For some, the romantic portrayal “normalized” the behavior; these subjects later registered a more permissive attitude toward stalking.  Similarly, a recent working paper found that when people were told that a xenophobic opinion they disagreed with was in fact a popular view, they were less likely to judge a person who publicly subscribed to it. 
More than simply destigmatizing the fringe, exposure to extreme opinions can change one’s sense of normality. When researchers presented more than 1,000 subjects with either radically conservative or radically liberal policy options—for example, ban immigration, or don’t limit it at all—their sense of what a centrist position was shifted toward that extreme. 
So yes, norms can shift to accommodate deviance. Of course, if Trump truly wants to be seen as “modern day” normal, a simpler route would be for him to move toward existing norms, instead of waiting for the norms to come to him.
 Bear and Knobe, “Normality” (Cognition, Oct. 2017)
 Lynch et al., “Tall Is Typical” (Memory & Cognition, Jan. 2000)
 Rakoczy et al., “The Sources of Normativity” (Developmental Psychology, May 2008)
 Schmidt et al., “Young Children See a Single Action and Infer a Social Norm” (Psychological Science, Oct. 2016)
 Centola and Baronchelli, “The Spontaneous Emergence of Conventions” (Proceedings of the National Academy of Sciences, Feb. 2015)
 Lippman, “I Did It Because I Never Stopped Loving You” (Communication Research, Feb. 2015)
 Bursztyn et al., “From Extreme to Mainstream” (National Bureau of Economic Research, May 2017)
 Simonovits, “Centrist by Comparison” (Political Behavior, March 2017)