This article is pure garbage. Your posting it and promoting its false claim is more of the Tea Party two step. And it illustrates the fundamental defect in your and Tea Party thinking and/or understanding of politics and how to make political arguments.
The monuments and facilities on the national mall are closed, but the grassy open areas in between remain open. So if the immigrants wanted to visit some of the national mounuments, they would have been denied, just as were the WWII Vets.
Here is a news program talking about how the monuments, bathrooms, trash pick up, and other governement services by the National Parks service (non-essential government) are shut down during the government shut down. It also shows how the national mall grassy parks and sidewalks remains open. Thus a protest or march, whether by the immigrants or by WWII vets or by Teapublicans would all be able to occur.
http://www.nbcwashington.com/news/local/Monuments-Mall-Could-Close-Tuesday--225874741.html