Q. Is there any religious problem with bringing a weapon into a synagogue?
In modern times no-one objects to the use of metal in building a synagogue or fashioning its appurtenances: the metal is being used for a constructive purpose and reminds us of the prophecy that swords will become ploughshares and spears will become pruning hooks (Isa. 2:4). Weapons, however, still represent the use of metal for destructive purposes, and this is inconsistent with the peace and serenity of the house of worship.
Leave the weapons to the security guards outside (if there are any), and trust in them (and in God) when you are inside the synagogue.