Another fine example of the peversity, or perhaps stupidity, of ethno-centrism. One group wants to celebrate an aspect of their ethnic heritage and another wants to do the same by preventing the first group from also doing it. There's a fascinating circularity to the logic.

A better approach might be for each faction to have their own parade, back to back along the same route, and draw straws to determine the order. Or perhaps the city could have a parade and give every body the opportunity to enter a float or marching unit, etc. Then after the parade, sell tickets to a giant "mud-wrasslin" pit in which the belligerants could make fools of themselves until the spectators died from laughing too much.