N/S PTO rules that "Redskins" is derogatory (not a case about the NFL team but likely precedent)

I think it is a fair analogy...although I recognize that our society has not yet arrived to the point where religion is as roundly rejected (regardless of context) as physical apperance generalizations, like "Redskins".
It's not even close.

How is "Saints" derogatory towards any group? Are there a group of very religious people who take offense to being called "Saints?" Was that term ever a term used as an epithet towards the offended group? What you're suggesting re:Saints and Atheists (or any religion that doesn't have "saints") is an outside group finding a term offensive. That's not the same -- it would be akin to Asians saying "Hey calling that team the Redskins offends me (because there isn't a team called the Yellowskins)." And again, the "offends" isn't because of a perceived slight, it is because the word "redskins" is in poor taste, just like we wouldn't have any team called the "Yellowskins" or "Blackskins" or "Whiteskins."

therefore offends them because it makes them feel to be second rate citizens, and generalizes that all citizens of the government either should, or do, follow that religion.
It doesn't offend Atheists (at least the vast majority of them) for those reasons -- it offends civil libertarians because it goes against the First Amendment. Atheists and others are fine when government allows such displays for all religions or non-religions, just when they deliberately restrict it to one specific religion is where it becomes a defacto government endorsement of that religion.

(You want to piss an Atheist off, tell them the US is based off of Judeo Christian values)
You don't piss off Atheists for that -- you just show that you're completely mistaken. the US is not based off any particular religion's principles.

One of my good friends is an Atheist
:9:
Just as the Washington Redskins would have to remove their name because the government recently (and officially) determined that it is offensive in nature, the Saints could potentially be forced to remove their name (or reject public funding) because the government has recently (and officially) determined that no religious speech, or imagery, can be associated with any entity that is either owned or funded with public tax dollars....all brought to you by lawsuits based on people being offended.
Nope. The Government cannot force a business to rename itself, no matter the "offense" taken. To think that the government would get involved in either of these issues is silly. And to imply that Saints is offensive to Atheists -- sillier.