There's a very important characteristic in politicians. They can act charming and friendly even with people who have maligned and insulted them, people they really can't stand with good reason. To be a good/professional/successful politician one must be able to swallow ego and pride at times.
When the Obamas had to host the Trumps, it certainly was difficult for all of them. The Obamas had both campaigned for Hillary by so seriously maligning Donald Trump that they definitely skirted or crossed legal barriers in the nasty things they said about him. But they did the proper thing, and Trump said all of the nice words, as if the negative malicious campaigning had never happened.
Donald Trump and his team have also been in touch with many powerful establishment Republicans, even though they did their best to sabotage his campaign for the Presidency. And, no doubt, quite a few powerful positions will go to them.
Donald Trump could never have built some of his massive projects, for example all of the changes to the West Side of Manhattan that had to be done for Riverside Blvd and the buildings there, if he wasn't a "politician."
To be a successful politician, one must be a pragmatist and be willing to work with everyone to achieve your goal.
