For sure. DOJ should strive for an image (and reality) of impartiality, and that would be harmed by having employees who can't let their politicized activities, even good ones, wait until after work.
Probably, but the biggest objection would come from the gays. They would say such an event shouldn't be allowed because it creates a hostile work environment and supports/promotes homophobia; it goes against the spirit of diversity, etc.