I agree entirely with Dale that denying a parade permit on content-based grounds — as the Mayor’s state reasons are — is unconstitutional, and clearly so. For nearly 70 years, the Court has made clear that the streets, sidewalks, and parks, even if they are government property, are generally “traditional public fora” on which the government has no extra power to impose content-based restrictions (beyond the usual First Amendment exceptions, such as obscenity, threats, and the like). The government may not refuse to allow a parade on the grounds that it doesn’t approve of the parade’s message. (The government isn’t even allowed to institute content-neutral bans on all parades, though it can impose some content-neutral regulations.)
The government need not allow banners on other parts of its property; but even there, it must act in a viewpoint-neutral manner when it comes to private speech — if it allows some speakers to put up such banners as their own speech (as opposed to expressly endorsing them as the government’s speech), then it can’t refuse access to other speakers based on those speakers’ viewpoints.
The mayor is of course not constitutionally obligated to issue any proclamation supporting the parade — but he is constitutionally obligated not to deny parade permits based on content, or to deny access to most other parts of city property based on viewpoint.
UPDATE: Dale Carpenter reports that “The mayor has reversed his decision and has now agreed to issue the parade permit.”