Each of us must decide this for themselves. I cannot go through life never dealing with those who hold beliefs antithetical to mine, but I can try. But blithely ignoring these bully pulpits has gotten us pretty far down the road we are on. Not just gun rights but that is beyond the topic here.
My answer is imperfect, because even today it is not possible to know everything. But if and when I know a company's position it is because they put it out there for me to know. And if a company chooses to hold anti-gun rights positions then I choose not to deal with them. I don't worry too much about the lists but they are at least a starting point. The information is out there to discover on my own. Examples are as I mentioned: Dick's will never see a dime of my money. I will no longer shop at REI.
As for NFL -- wasn't there some kind of game yesterday? Not really sure. I was busy smoking ribs for a family dinner and doing a woodworking project with my daughter. My son came down from college, and my brother in law and fiance dropped by. We complained about ammo prices and I showed my son the new boot grip on my NAA mini. Ribs turned out really good, I'm happy to say.
Yes it's a rabbit hole. So I just do the best I can to support pro-gun or at least nonpartisan companies. To your broader point if I know a company is exploitive or is in some other way immoral, then yes; I look for other places to spend my dollars. It isn't that hard.