N/S PTO rules that "Redskins" is derogatory (not a case about the NFL team but likely precedent)
It's not a fair analogy at all. The idea isn't that some threshold amount of people find the name vaguely offensive for some reason. The conclusion of the agency here was that the name was disparaging to a group of people. While "Saints" has a religious connotation, it isn't disparaging or derogatory. It doesn't have a negative connotation or history with respect to those it implicates.
The idea isn't some entirely subjective concept of offensiveness. That could never lead to any applicable standard. Magicians could protest the Orlando Magic. Zookeepers and naturalists could protest any team with an animal name.
That's not what is happening here.
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".
This whole conversation got started because a government agency made a decision to reject a NEW company's brand, because our current day society finds the term (regardless of the context it's used in) offensive to a group of people. The question then became, will this set precedent that would require an OLD company's brand (that was given when it was NOT socially inacceptable) to change it...based on current social standards.
Similarly, there have been court rulings (government agency) that have sided with Fredom from Relgion groups, in their efforts to get displays of religious imagery removed from land, or from facilities that receive public funding...on the grounds that they feel any governmental interaction with said religious symbol represents an endorsement of that religion, and 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. (You want to piss an Atheist off, tell them the US is based off of Judeo Christian values)
In both cases, the initial context & meaning of those symbols are being ignored, in favor for how people of today interpret them to mean.
One of my good friends is an Atheist, and a warrior for the cause, and would completely disagree with you about Christian religious imagery not being offensive, or negative in historical context. We had to go to bar rules when hanging out because every time religion was discussed, he would bring up the Crusades, all the death & bloodshed at the hands of religion, peodphelia, discrimination, etc. He meets with a group of like-minded people on a regular basis, and there is a nationwide network of similar groups.
Where the analogy ties in is that in both cases, recent legal precedent could be used to force organizations to change, and come into compliance with modern day social standards. 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.