The speed of light in a vacuum being [constantly and universally] constant is an axiom (ie assumption, belief) of special relativity so it applies to inertial frames of reference.
So, strictly it is not "regardless of your frame of reference". Accelerating frames, eg rotating or accelerating (eg under gravity where General relativity applies) require special treatments.
So, strictly it is not "regardless of your frame of reference". Accelerating frames, eg rotating or accelerating (eg under gravity where General relativity applies) require special treatments.