But wouldn't that violate the Constitutional right to free speech and the peaceably assemble?
Yep. But for the details, let's check the law.
What Price Protest? : Marquette University Law School Faculty Blog
The requirement that a fee be paid in advance of the exercise of First Amendment rights constitutes a prior restraint on the exercise of free speech. See Forsyth County, Ga. V. Nationalist Movement, 505 U.S. 123 (1992). Advance fee requirements are recognized as a prior restraint because some individuals will forego the exercise of their rights rather than apply for advance permission or pay the fee. Prior restraints on the exercise of free speech are highly disfavored under constitutional law. While they are not per se unconstitutional, prior restraints will be subjected to heightened scrutiny. The Supreme Court has articulated the following standard for evaluating the constitutionality of government permitting schemes:
Even in a public forum the government may impose reasonable restrictions on the time, place, or manner of protected speech, provided the restrictions “are justified without reference to the content of the regulated speech, that they are narrowly tailored to serve a significant governmental interest, and that they leave open ample alternative channels for communication of the information.”
Nathan Kellum, Permit Schemes: Under Current Jurisprudence, What Permits Are Permitted?, 56 DRAKE L. REV. 381 (1985).