Eugene Volokh has flagged a case in which a Christian group dedicated to converting Jews alleges that it was barred from leafleting on the public streets. Assuming the truth of the allegations in the complaint, I agree with Eugene that the group's First Amendment right to distribute literature may have been violated.
As I explained in an interview relating to a similar case, leafleting has long been granted special constitutional protection. In part this relates to the historical practice, prior to the development of the institutional press, of conveying messages by leaflets or pamphlet. Protection is also granted to this means of communicating owing to the need to guarantee that even the "poorly financed causes of little people" have some means of reaching a public audience. It may seem outdated in the digital era, but leafleting remains an important means of communicating information in public places.