I realize that some of the issues are cloudy and have been muddled over time but I dealt with a lot of this stuff when I was in politics as many of the issues we dealt with were controversial. I have also dealt with 2nd Amendment issues many times. The single biggest reason you don't find many people or businesses pursuing these cases is because many of the lower courts are a crap shoot and you end up having to take it all the way to the Supreme Court which takes mucho dinero and attorneys wanting to challenge.
The FCC prohibits a lot of speech and images. As a government entity, they pretty much make whatever rules they want. In my opinion, they have long ago surpassed their constitutional limits.
however, I think we are discussing different things here.
The network or the NFL, based upon their contract between each other, can ban any commercial on any subject as long as they aren't discriminating against a protected class. Gun owners are not a protected class. If they said Asians can't advertise, that would be a civil rights violation. If they say fast food companies can't advertise because they think it's bad for you, it's completely legal. They control that show and network and it's content as long as it's within the FCC regulations and doesn't violate the civil rights of a protected class.
The constitutional rights belong to the person who owns the rights to broadcast, not the advertisers. I can't walk into Walmart and advertise my business. I can't stand in your yard in an ape costume and advertise my business. I can't make the Goodyear blimp advertise another tire company.
The only Dish / DirecTV suit I could find was based on the claims made in the ad being fales, not that they weren't allowed to advertise over DirecTV through the networks.
Gun owners are not a protected class. You're right. You also are right that they can say we will not accept certain advertisements. But it is the rationale that comes into question. Is it what they are saying? Or is it about a thing? I don't know if and on what grounds the NFL supposedly turned down this commercial. It would have a lot to do with whether they have the right to do so. In most cases - the simpler the better.
The decision in the Dish v Direct case was based on the fact that Direct was allowing cable companies to advertise but trying to deny Dish. Part of the reason for the decision was that they were using the public airwaves. Advertising is tricky though and you do have to ensure that you are not denying while allowing something similar in nature.
The link you provided is an opinion but not necessarily based on precedent. I can deal with what I have seen.
I think we are talking in circles here. I don't know what requirements the NFL has given to its networks nor how they are stated. All I'm saying is that if this was truly a case about the NFL taking an anti 2nd Amendment rights stance, they could be sued on those grounds. I don't buy the whole thing and think it is just internet lore designed to pit people against the NFL. There's just something missing.
You don't have the right to go into a Walmart and advertise any business whether they have allowed advertising by other business inside or not. If Walmart however, allowed someone to circulate petitions inside their doors and then told someone else they couldn't based on what they were circulating, they could get sued. Outside? That depends on what they have done historically and if they allow any other similar kinds of uses of their "public" area.
A similar issue was the reason Target decided to say no to the bell ringers. They consulted with Constitutional attorneys and determined that if they allowed the Salvation Army to use their store fronts to solicit, they couldn't refuse others that would like to solicit in front of their stores. The Salvation Army solicitors as a group are not protected by the Bill of Rights. The decision was to have a no soliciting policy that applied equally to EVERYONE. Failure to do so would allow anyone to use their store front to solicit what ever they wanted - be it charitable or for profit. Why? Discrimination based on content. As a result, our petitioners could not circulate in front of Target stores but could in front of other businesses that did not establish this outright policy.
Anyway, none of this really matters. As I said before, I'm pretty sure Goodell et al know the laws and already anticipated this kind of issue before refusing the commercials if they did indeed do so. It's why attorneys get paid.