Can I Say Birkat Kohanim While Carrying a Gun? - Sources for Episode 113

(22) And if you make for Me an altar of stones, do not build it of hewn stones; for by wielding your tool upon them you have profaned them.

9) R. Shimon b. Elazar says: Iron was created to shorten a man's days, and the altar was created to lengthen them. It is not fit that the "shortener" be lifted over the "lengthener."

(7) When the House was built, only finished stones cut at the quarry were used, so that no hammer or ax or any iron tool was heard in the House while it was being built.

(4) Just as it is prohibited for a woman to carry out certain items unique to a woman into the public domain, the Sages said that a man may neither go out on Shabbat with a sword, nor with a bow, nor with a shield [teris], nor with an alla, nor with a spear. And if he unwittingly went out with one of these weapons to the public domain he is liable to bring a sin-offering. Rabbi Eliezer says: These weapons are ornaments for him; just as a man is permitted to go out into the public domain with other ornaments, he is permitted to go out with weapons. And the Rabbis say: They are nothing other than reprehensible and in the future they will be eliminated, as it is written: “And they shall beat their swords into plowshares and their spears into pruning hooks; nation will not raise sword against nation, neither will they learn war anymore” (Isaiah 2:4). With regard to women’s ornaments, they added that a garter placed on her leg to hold up stockings is pure and cannot become ritually impure as a utensil, and she may even go out with it on Shabbat. However, ankle chains, which were also women’s ornaments, can become ritually impure, and she may not go out with them on Shabbat.

It is written with regard to Pinehas: “He arose from amidst the assembly and he took a spear in his hand” (Numbers 25:7). From here, where it is written that he took the spear only after he arose from the assembly, it is derived that one does not enter the study hall with a weapon. The assembly in this context is referring to the seat of the Sanhedrin. Pinehas removed the blade of the spear and placed it in his garment [be’unkalo] and held the shaft of the spear like a walking stick, and he was

It's permitted to enter the synagogue with one's staff or satchel or backpack (meaning, purses - the Targum has backpack to be briefcase). Some forbid entering with a long knife or with it's blade uncovered.

Speaking of that verse in Isaiah, the Gemara cites that Rabbi Yoḥanan said: Any priest who killed a person may not lift his hands in the Priestly Blessing as it is stated: “And when you spread forth your hands I will hide My eyes from you…your hands are full of blood.” Here we see that the Priestly Blessing, performed with hands spread forth, is not accepted when performed by priests whose “hands are full of blood.”