It's open to the public to see. Every group that runs a St. Paddy's Day parade is a private group. To be a member of AoH requires to be Irish or of Irish ancestry and they collect dues. No different then an Eagles Club, Moose club or Elks club.
They pay for the services of the Government. Basically they are renting Government services. When Government services are rented they are defined as a private event. Like a motorcade for a funeral.
Here is another example of St. Paddy's parade being paid for privately, all of it.
Heya AC.....the event in Boston was sponsor by the South Boston Allied War Veterans Council.
Sam Adams beer manufacturer pulls out of South Boston St. Patrick’s Day parade
We were hopeful that both sides of this issue would be able to come to an agreement that would allow everyone, regardless of orientation, to participate in the parade,” The Boston Beer Company said in a statement. “But given the current status of the negotiations, we realize this may not be possible. We share these sentiments with Mayor Walsh, Congressman Lynch and others and therefore we will not participate in this year’s parade.”
This week, Boston Mayor Marty Walsh attempted to negotiate a compromise with parade organizers, which would allow a gay veterans group to march in the parade. The parade, which takes place on March 16, is organized by the South Boston Allied War Veterans Council.....snip~
This week, Boston Mayor Marty Walsh attempted to negotiate a compromise with parade organizers, which would allow a gay veterans group to march in the parade. The parade, which takes place on March 16, is organized by the South Boston Allied War Veterans Council.
Negotiations between Walsh and the veterans council reportedly broke down on Thursday. For its part, the council claims LGBT Veterans for Equality planned to march with only one actual veteran.
But even before the permit was rescinded, the group was saying the LGBT group could participate only as long as it did not include the word “gay” in any of its materials or clothing.....snip~
Sam Adams beer manufacturer pulls out of South Boston St. Patrick
As you can see from Sam Adams own words. The LGBT community activists are the ones that refused to negotiate.