There is more than a slight difference between your cell phone and your gun.
No, in terms of legalities and wording of this sign, there does not appear to be. If there was intent to differentiate cell phones from guns the sign would not include both in the "no use" language.
The sign says "no use of cell phones" and "no use of guns".
How in the world do you interpret that sign to mean that cell phones may be carried but not used, but guns can't be used OR carried?
You can't. You cannot have it both ways.
So, if you think this sign says you can carry a cell phone, then you can carry a gun. You just can't use either one without violating, at least, the terms of the sign.
Words matter, especially in the law.
What you "feel" about this makes you sound like the typical anti, going on "feelings" rather than facts.
The sign says ""We restrict the use of sunglasses, cellphones and firearms while in the bank."
Since the sign does not explain what the exact restrictions are, and does not say "please contact manager for info" or some other disclaimer, then we go solely off the language of the sign which says "use".
It restricts the "use" of sunglasses, cellphones, and firearms equally to anyone who can read English without adding emotional context.
Therefore, a "reasonable person" (the basis for most law) would in my opinion interpret the meaning to apply to all things equally, and since it's silly to think a bank would prohibit a customer from carrying his cell phone in his pocket, it is equally silly to think that the bank is trying to prohibit the carrying of a legal gun.
If you DO interpret the word "use" to include carrying, then you MUST apply that restriction to all items and leave the cell phones and sunglasses in the car with the gun.
It's even more silly, bordering on just plain insane, to interpret the sign to somehow have DIFFERENT meanings of the word "use" for the different items simply because of the emotional impact of the items.