Nonetheless, how users should react to private company decisions such as this is an interesting and important question; and it will also be interesting to see how Twitter applies its policy to other political ads.
Disclosure: I have argued, in a paper commissioned by Google, that search engine results are protected by the First Amendment; see also Zhang v. Baidu.com Inc. (S.D.N.Y. 2014), which takes that view. But the First Amendment analysis here doesn’t rely on the argument in that paper; the right of a content provider to refuse to publish political advertising that it doesn’t want to publish is pretty straightforwardly recognized.
UPDATE: Twitter has reversed course on this:
Our ads policies strive to balance protecting our users from potentially distressing content while allowing our advertisers to communicate their messages. Nowhere is this more difficult than in the realm of political advertising and the highly charged issues that are often addressed therein. After further review, we have made the decision to allow the content in question from Rep. Blackburn’s campaign ad to be promoted on our ads platform,” a spokesperson said in a statement….While we initially determined that a small portion of the video used potentially inflammatory language, after reconsidering the ad in the context of the entire message, we believe that there is room to refine our policies around these issues.