This is really interesting. Obviously, the organizers of any event can choose who can march in it and governments provide security for all kinds of exclusive groups such as the KKK in the interest of good order. The question I have is what or who put the idea in Merc's head that the holiday wasn't about organized labor? Is it a concerted effort to "disremember" or happenstance. This isn't one of those issues where there are competing narratives,.. yet. Make believe history is pretty easy to spread if people want to believe something different.
http://en.wikipedia.org/wiki/Labor_Day
The first Labor Day in the United States was observed on September 5, 1882, by the Central Labor Union of New York[1] It became a federal holiday in 1894, when, following the deaths of a number of workers at the hands of the U.S. military and U.S. Marshals during the Pullman Strike, President Grover Cleveland put reconciliation with the labor movement as a top political priority. Fearing further conflict, legislation making Labor Day a national holiday was rushed through Congress unanimously and signed into law a mere six days after the end of the strike.[2] The September date originally chosen by the CLU of New York and observed by many of the nation's trade unions for the past several years was selected rather than the more widespread International Workers' Day because Cleveland was concerned that observance of the latter would stir up negative emotions linked to the Haymarket Affair, which it had been observed to commemorate.[3] All U.S. states, the District of Columbia, and the territories have made it a statutory holiday.
If anti-union GOP lawmakers wanted to march in a pro-union event and I was the organizer. I'd welcome them, every group needs a foil. Unofficially I'd say break out the rotten eggs and fruit.