Shinzo Abe's killer, Yamagami Tetsuya, told investigators that there was no political motive behind the killing. He referred to a new religion, with which the abbey was closely associated. The cult cheated Yamagami's mother for financial gain.
See, Japan is a country where even getting a bird hunting weapon requires a 13-level permit, which is only valid for three years. There, Yamagami fires a firearm of his own making. It is impossible to collect all the materials needed to make a weapon at home and to arrange proper double firing. It is not possible to go so close to the Abbey with a firearm.
Yagami's gun was a patchwork of tape and metal cylinders. Some gunpowder was used to ignite the odd type of bullet. Yamagami took out the weapon and fired it very quickly and easily. It is impractical for an unprofessional person to make a weapon suitable for emergency use, carry it to a suitable position, and shoot it past alert guards.