Donald Trump's campaign was marked by extreme rhetoric and out-of-control rallies. His discussed Presidential plans include punishing women who have abortions and requiring all Muslims in America to register themselves. A president should espouse and model inclusion rather than derision. In his acceptance speech, Mr. Trump said that the time had come for Americans to look beyond their differences and come together to heal the country. It remains to be seen whether this will actually take place, but his acceptance speech suggests that he may adopt a more moderate tone when in office. If he keeps that promise, that would require Trump to adopt a traditionally Republican stance, which could perhaps enable the country to heal rather than drifting to even further polar extremes.
Trump's nature is not derived from political ideals. After he won the nomination, he did not act like a traditional Republican. Instead, he did what he's always done and acted like himself. So, it does not make much sense for him to act like any other politician, since he broke the political rule-book by winning.
Traditional Republicans are what the people voted against. The Republicans had so many traditional Republicans to choose from. Rubio, Christie, Bush, and the rest all could have been that choice. Americans made it clear that it is not what they wanted. Trump should be true to the people who elected him and behave in a non-traditional manner.
Under no circumstances should Donald Trump act like traditional Republicans now that he is president. The very reason that Trump won the election is the direct opposite of traditional Republicans. People are sick of traditional establishment Republicans, and Democrats, for that matter. If Trump does act like a traditional republican he will be a one term president.