Yes, those types are the ones who betray by their behavior that they actually do believe in God. If they didn’t, they wouldn’t care if He was mentioned in the public square, anymore than they care if people mention the Easter Bunny. They only care because they secretly know God is real, but they do not want to be reminded of it.
I think most fit this category.
I think a few really do not believe in God and do not like the idead of society pushing what they consider a lie on others. They would be more believable if they also fight to stop other actual lies like global warming and speak out about stealth muslim jihad by immigration in their countries, and stuff like that. But I believe this percentage of atheists is very, very, very low.