I certainly don't. The reality is that to make a Civil War park acceptable to all, it should be for all. If we as history lovers are given all this wonderful green space, I'm not sure we have a right to say "you can't use it if you don't feel the proper amount of deference". It's a park, paid for by the American public, all of which should have equal accesibility to it.
I DO have a problem with dog-walkers in parks that don't clean-up after themselves, but I guess that's a different story.
Edit: I would also add that there's nothing I'd like to see more than hundreds of people engaging in other activities on Saturday, whether they be Civil War related or not, while totally ignoring the hooded fools. Make it clear that they're as insignificant as we know they are.
Aren't cemeteries paid for and kept up by the American public?
And technically, with all of the CWPT involvement and other preservation organizations, not all of a park is paid for by non-CW buffs.