It's not a bad idea, I'd actually favour it myself because "screw all this noise", you know?
But there are a few issues.
First, practically, you now have to decide what is "political". Is an ad for abortion services political? What about the NRAs latest membership campaign? Or a gun safety campaign? Lots of things are political to at least someone. So who decides what's political? You're still in something of a mess. And you technically have to ban ads that are entirely factually true now!
Similarly, even if you can stop the ad next to a celeb tweet being political, can you stop the same buyers paying celebs to Tweet fake news directly or Russian bots creating 10,000 accounts and tweeting fake news? Will you go through @Potus tweets and cut out the fake news? Suddenly the Liberal media is eating trump babies.
Second, it doesn't solve your core problem: traditional media, from the guardian to fox, will now attack you for being anti free speech (AND for every time an ad gets through your filter, that looks like it shouldn't). They don't actually care about whether you publish fake news. They publish it. They just want you to die. Plus now you've offended your freedom loving users, and alienated the politicos relating you. Maybe under the 1st amendment US politicians can't FORCE firms to take their ads. But they can audit them, drag them I front of Congress, cut net neutrality so ISPs eat their profits etc.
Ultimately, its down to users to filter their media and fact check it. It always has been. There was never a golden age where newspapers reported facts in order of importance and politicians were honest and policy fact driven. But no one wants to admit that. Facebook made that mistake, it was reported as "Facebook will publish fake news, eat babies, fuck your wife"