If someone were to equip their strifekind with a toy/replica weapon, would it become real? In one of my fan ventures, one of the characters equips one of those costume props and it turns real.

Don’t see why it would, you may be able to allocate it but you’d still be using them as useless toy replicas to clobber people with. Captchalogues store things and let you retrieve them, they don’t exactly bend reality more than being a pocket storage dimension. If anything, much like Dave’s ½ sword specibus, it may force the Strife Specibus into a Fake Weapon version of the specibus.