I believe the OP ws asking bout getting the signs removed for everyone, not himself carrying at work.
In that light, it is a real political hazard for you. No matter what the dispute resolution process is at work, if you advocate for the removal, you will have labeled yourself as someone who MAY be violating company policies and carrying anyway, a single anti-gunner in the process can make your life very bad aka search your car or firing you for refusing etc, it depends upon company guidelines.
Least politically dangerous method, everything posed as a question and no educational efforts imposed upon them. Questions like:
"Mr Jones, I just saw those new signs, I have herd gun owners can be real finicky about them and actually boycott business places that post publicly, are we sure in this economy they won't do the same thing to us?"
What you have to likely understand, SOMEONE suggested they post, if it was the company lawyer, you are not changing the mind, it is a liability issue and lawyers argue for a living, they also play for the win no matter how small and if the owner is the judge, the lawyer will hold more merit with him than you likely. If the owner or CEO is an anti, it is a lost cause on many levels and likely not worth the effort. If by chance it was some anti employee suggestion that holds only as much merit as you, IMHO you have a fighting chance if you can some how tie it to a loss of business.
From a very real perspective, most companies dealing with the public try and put forward a politically neutral front, except on guns. That can also be used, simply ask the question "Mr Jones, noticed the sign, is that some sort of political statement?"
Notice that in both instances, you have not impose a view, you have not even officially given a thought or position, you have asked a question of Mr. Jones that makes the answer HIS, he has ownership of the suggestion of removal because of one of the two theories, loss of business from owners or political foes, you only planted the seed, its not your plant so to speak.
Ownership of an idea is key in getting things implemented, but you must have the power to indeed say yes. If you do not have that power, you need to give ownership of the idea to one who does, if they have ethics, they will give you at least partial credit for fostering the idea they perfected. IMHO this is one of the major problems that develops in corporate politics, there might only be one person whom can say yes, but there is a boat load who can say no and get in the way of any idea and some will if they simply can not tag onto a good idea themselves.
This all only applies if you like and want to keep the job or in a more specific corporate battle ground, if you are at odds with the one who suggested the sign in the first place, you can take very aggressive tact (difference in aggressive and assertive and aggressive gets enemies for life), you simply wait for the right moment and the right person and you say something with a sting like "Wow, I just saw that, have you noticed that sign? What nutjob decided it was a good idea to run every gun owner off from doing business with us? My gosh more than 50% of the people in this country own guns!"
Huge risk in that last one and if you do not know your audience, you are in instant trouble if you deliver it.
Food for thoughts on how one can grasp the rungs of the ladder in corporate America, applies to lots of things beyond something as volatile as guns, but they are the same in process, the sign is SOMEONE's protected turf, SOMEONE else with more power in the structure has to present the idea, let the idea be theirs and it just might work.