Non-Americans who have been to the US.. What is the weirdest thing about America that Americans don't realize is weird?

In some states, these signs don't even mean that a person can't carry a concealed weapon into the shopping center. In my state, for instance, assuming you are otherwise able to legally carry a gun (meaning you took a class and aren't a felon), the list of areas where you can't legally carry a gun is very limited: Federal buildings, courthouses, etc. If a business has a sign posted stating "no guns allowed," you can still legally carry your weapon in that business. If an employee sees that you're armed, they can ask you to leave, and you're trespassing if you refuse, but nothing legally stops you from carrying a gun into the establishment in the first place.

As a disclaimer, I'm not arguing this one way or another. I have a license to carry a concealed handgun, in fact. Just sharing information.

Yeah I'm sure minimum wage clerks are going to totally feel comfortable asking the armed person (someone who believes they need to arm themselves to enter a shopping center) to please leave.
- Yeah I’m sure minimum wage clerks are going to totally feel comfortable asking the armed person (someone who believes they need to arm themselves to enter a shopping center) to please leave.
  
  yeah, they probably would. Shooting someone is very fucking illegal.
  
  also most larger establishments are going to have security, and, you can call the police if you wish.
- Most people who have a concealed carry permit are generally law-abiding. I would certainly leave immediately if asked.
If a business has a sign posted stating “no guns allowed,” you can still legally carry your weapon in that business.

I'm sure that's the practicality, but I am skeptical of the legality of a CCW permit trumping the rights of the property owner.

It sounds more like breaking the law and just not getting caught. Do you have any links to CCW permit overriding property owner rights?
- Property owner rights do not magically override the 1A.
  
  Property owners are welcome to write scary notices. They are just not legally enforceable.
- I don't know the statutes offhand; I'm basing this on what I was taught in my CCW class years ago.
  
  The general idea is that the state sets limited laws on where you can't carry concealed. Government buildings, etc. These restrictions hold the force of law. For a private property owner, they can certainly say "no guns," but it has the same legal weight as if they said "no hats." They can set rules for their property, but those rules don't magically become law. That's where trespassing laws come in; if you're asked to leave, they have the right to ask you to do so.
  
  Some states do have laws in place stating that "no guns" signs are legally binding, but the signs must meet certain legal criteria as far as wording. Surprisingly, I think Texas is one of these states, but I could be wrong.
  
  My state is solidly blue, so it does seem strange to me that the laws are written as they are.

Does this give you any increased sense of security as a non-american?

the opposite for me
The sign actually would give me an increased sense of security yeah.

Obviously a lunatic out to do a mass shooting would disregard the sign but your average gun wielder might be offended and take their business elsewhere – and statistically that's the one who's more likely to shoot me. That's my logic as a Norwegian who's lived there for just a year anyway.
- and statistically that’s the one who’s more likely to shoot me. That’s my logic as a Norwegian who’s lived there for just a year anyway.
  
  what for though? are you just harassing people in public? I don't understand why someone would be concerned about someone just having a gun. You probably won't even see this person, let alone bump into them, let alone get into an altercation with them.
  
  And most of them are sane and reasonable people who understand how de-escalation works.
  
  The question was whether or not a sign saying guns not allowed at a mall would make me feel more safe there. I would see them, I might bump into them, it's a mall. The argument that most of them are sane and reasonable doesn't reassure me much when we're talking about people with a magic kill button.
  
  i guess my point that you aren't picking up on here is that this is quite literally an irrational fear. You should be more worried about being hit by a car, or punched in the face. Or falling down a set of stairs or something.
  
  I've been punched before, complete blind violence. The difference is that being punched didn't kill me. The fear of getting shot in America is not irrational. Again refer to the page full of statistics in my previous comment.
  
  being shot doesn't have to kill you either. A lot of people survive being shot, lots of people also die from getting punched.
  
  What if they had a knife? Those aren't exactly hard to get, knives arguably cause more violent injuries than guns do. Unless you're shooting someone point blank with a 45 or something.
  
  Ok now I know you're just full of shit and can be safely ignored, thanks.
  
  ok
Hmmm. Not overly, I assume it's just a "suggestion" but am not sure. But I have had to travel there quite a bit for work, and I usually feel mostly secure. But I am aware a lot of people carry them in the US, and mostly just keep to myself moreso than I normally would outside of work things.
- In a few states it's a law but mostly it's a suggestion and at worse you'll get kicked out. I know New York has a law and maybe California.
  
  Interesting. I had no clue. Thanks for the info.

Never seen this where I live. Not every state is a complete shit hole thankfully

I haven't seen it many times, but the first was definitely a bit surprising.