This movement does not care about anyone's First amendment right but theirs ( Mayor Quan in Oakland was not permitted to address a group of protesters because they boo her out).
That said I don't think the City of Chattanooga will be able to evict the protesters from public parks even with the curfew laws already in the books. A flat curfew that prohibits such (peaceful) activities after a certain hour would not hold water at the Supreme Court Level. The City of Chattanooga would not win this case.
Let's see what happens...