I see it somewhat differently. As you noted keeping religion out of gov't and ed is a legitimate policy goal, but the folks who are shoehorning it in are doing so aggressively. Take Hobby Lobby for instance. They support atheist China for their cheap goods that they sell, then turn around and tell the women in America who work for them that they will decide which healthcare is available to them based on their sincere dedication to their lord and savior. Oh, yeah, then they get nailed by the NY Atty General for false advertising with their "permasale" schemes. They are no more dedicated to Christ than an atheist but they use their faith to drive public policy.
I find that action quite aggressive. Same with any of a hundred other examples not including the whole Religious Right's war on women and abortion rights. We have several SCOTUS justices who actively lied about their adherence to stare decisis just so they could get on the court and then gut Roe.
That level of aggression is not acceptable and I suspect you and I both agree with that position. But it is aggressive. The religious have been quite vocal and aggressive and the atheists have, what, 5 "famous" vocal adherents? Sam Harris, Dawkins, Hithchens, and maybe a couple others...vs entire swaths of organized religion that fight daily and loudly to stand up for their faith and aggressively push it.
Personally, when I was in the process of "de-converting" from Christianity it helped to have a voice like Sam Harris or Dawkins. Now that I'm a bit longer in the tooth as an atheist I can definitely see Dawkins as being kind of a nasty anti-theist, but it doesn't change the point.
I am not an aggressive atheist in real life (I may play one from time to time on here) and as I said I actually have mostly Christian friends. I even see a lot of value in the faith. I don't, however, think that one side has the right to proselytize while the other side has to sit quietly by. And vocal folks on any given side can be a benefit to the side if only to help those who are timidly exploring a position to realize that, indeed, they are ALLOWED to think the "bad thoughts". That maybe the "bad thoughts" aren't bad after all.
Just my 2cents.