Catholic ping!
To me, it seems pretty damn simple for the Catholic Dioces in this case.
Disavow the Parade.
To continue to support it, aid in its organization, or attend it, is to affirm not only political picketing by those who despise Christ, but also it completely dishonors the saint being venerated.
The solution is clear, if a bishop has the balls. DISAVOW THE PARADE
Believe it or not... This has huge legal implications down the line.