Fallon is not apolitical at all. He had Chris Christie on during the unfolding of the Bridgegate scandal, let Christie say whatever he wanted, and didn’t question him about it at all. They even did a stupid dance together.

And then he had the infamous ruffling of Trump’s hair, which I hope clings to him for the rest of his life.

In both of these instances, Fallon had powerful political figures on his show, and he gave them unfiltered access to his audience, letting them deliver whatever message or impression they wanted. 

By giving these two men (and others) this platform and opportunity, on the public airwaves, Fallon took an explicitly political position, and that position was “whatever these guys want you to believe is true, because look at how much fun we’re having! Let’s lip sync now!”

He may never overtly express a political opinion, but Jimmy Fallon is anything but apolitical.
Christie to lawmakers avoiding town halls: Go do your job
New Jersey Gov. Chris Christie says Republican lawmakers should hold town halls even if that means confronting hundreds of angry progressive constituents.
By Eric Bradner, CNN

“Now that Republicans control the House, the Senate and the White House, they’ve gotten what they asked for, he said, so they have to accept the consequences, including rowdy protesters at town halls. ‘I understand why members of Congress don’t like it,’ Christie said. ‘But you know what? You asked for the job. Go do it.’”