As an observant Jew, we don't carry anything on our Sabbath (Friday at Sundown until Saturday at sundown). Keys, wallet, guns, nothing.
Yes and no.
First, a few quick definitions so our non-Jewish and less observant Jewish friends can follow this:
-Eruv: There is a principle in Judaism that one cannot generally carry any item (even a house key) outside of your house unless in a fenced in property or public courtyard on the sabbath. There is an exception, if the area has something called an eruv. Most
major Orthodox communities and some minor ones in the US have eruvim (the plural of eruv). I mention Orthodox here, because outside of Orthodox Judaism few Jews follow the laws involving eruvim.
-Muktzei: On shabbos (the sabbath) we are not permitted to handle any item that can only (generally) be used to do something that is forbidden on shabbos. On shabbos we cannot drive, thus under the laws of muktzei we can't handle car keys on shabbos. Guns cannot be used (outside of self defense situations) on shabbos without breaking numerous laws so guns are muktzei. However, this prohibition is fairly "minor" and thus it is pretty easy to get a heter (an excemption) for things like, carrying a gun, if the situation warrants it (one would need to go to a rabbi who is expert on this aspect of Jewish law).
So if one isn't within an eruv, there isn't much one can do. They cannot carry anything out of the house. However, within an eruv one can carry pretty much anything that is otherwise allowed.
However, it sounds (from your other examples) that you are speaking of items that are muktzei. Even more major laws can be broken when a life is at stake. A heter for something more minor, like muktzei, takes a much lower standard. In Israel for instance there is a general heter that allows frum (religious) Jews to carry firearms on shabbos. Here in the US, it would probably depend upon where you were located, but since most Orthodox communities (again, the only ones who really follow these laws) are located in major cities, often in some not so nice neighborhoods, it probably wouldn't be hard to get that heter. I know in Baltimore several Orthodox shuls have members who are supposed to carry guns to provide security to the synagogue, most at the request and not just with the permission of the rabbi. Of course, since the general principle is that guns or knives wouldn't be allowed on shabbos, that isn't necessarily true in a good many cases (again, if you are Jewish and thinking about carrying your gun on shabbos check with a rabbi expert in this area since a lot depends on your locality and your specific situation).
So, while true in principle, your statement isn't 100% correct about guns.
Now another potential stumbling block is that weapons are not allowed by Halacha (Jewish Law) into the sanctuaries of synagogues. The idea is that weapons are meant to destroy life (even if it is in defense) and prayer (which is what is done in the sanctuary) is meant to protect it and so these are at cross purposes. Out of respect one should not bring any weapon into the sanctuary. However, if one must carry a weapon and can't leave it at home (you live in an unsafe area, or your job requires it) there are two possibilities. The best is to find a secure place to store it in the lobby of the shul (or in your car if it isn't shabbos). The other possibility is to bring it into the sanctuary with you but then you are required to keep it covered and concealed, you should never have it in the open in the sanctuary of a synagogue.
So, again, while in principle the ideal is no guns in shul, in practice that isn't always what is required. In addition to life being paramount in general (and thus, if you are in an area where the need to defend it may come up you should have the means to do so), even many of the specific situations where things
could get sticky are pretty much covered and you could be OK (again though, it does depend upon your locality and your specific situation).
For everyone else, I apologize if this post seems a bit "technical". While I kept it as basic as possible, I realize many/most here have little interest in the nuances of Halacha (Jewish Law).