The yield stress of a material is a physical property. I don't see how this property can vary depending upon what the Code is.
Of course, material specifications are defined under many different systems and there is no assurance that a steel under an ASME material specification is identical to another steel produced to a different specification. But if the two specifications are "equivalent" then the steel itself should have one given yield stress as a physical property. But under ASME Code the minimum yield stress is defined. If I remember correctly, some European standards also define a maximum yield stress in order to assure ductility (the maximum yield stress of the material should not be too close to ultimate).
Also, other things being equal, I would think that a steel product with higher yield stress would be "safer" than one with low yield stress. It's a relative measure of the quality of the material. Advances in metallurgical processing over the past 100 years means that the steels of today have higher yield stress values than older steels, and yet are of better quality, better consistency, and hence "safer". JMO
Regarding ASME as a "law". No, it is a design code, not a "law" in the sense of a legal, regulatory jurisdiction. In North America a number of legal jurisdictions have adopted the ASME Boiler and Pressure Vessel Code as a standard for pressure vessels operated in their jurisdiction: any such vessel must meet ASME requirements. But ASME itself is not a legal jurisdiction and cannot enforce the Code under a legal system (they will enforce it through the Code stamp registration process...you don't comply, you don't get to sell ASME-stamped pressure vessels). For example, in the EU pressure vessels must comply with the PED under the authority of the legislative (law) process. But the PED is not itself a design code, numerous design codes are accepted under the PED.