Einstein told us that the speed of light must always, not only appear, but BE the same in every frame of reference no matter how fast we are moving towards or away from it. So even if you are moving at half the speed of light towards a light beam, the entire universe must conspire to either "speed up" or slow down your "time" to account for this difference.
If that makes sense to you, you are no longer sane. You cannot create scenarios of two mutually exclusive events at the same time and call that reality. This is fundamental to reason.
To show this contradiction, consider you are running away from a light beam and towards another at the same time. You move at half the speed of light. Of course in real life you will encounter the light you are moving towards first, but in Einstein's universe both beams MUST (in your world) hit you at the same time. However, in Einstein's universe, someone else will see them hit you at different times because they also MUST see light travel at a certain speed. This is just plain fucking stupid.
At best you can have an illusory effect, but to confuse that with a real difference in simultaneity is to truly give up on reason itself.
Your reference frame and my reference frame differ infinitesimally. The very act of motion with respect to the observer changes the reference frame. This is basic stuff, man. It’s self-evident even on the macro-scale.
That's not separate realities though. You've described one reality and one person moves in it and calls it his "frame". So what?
Einstein's theory about relative simultaneity is from his imagination. No experiments confirm that claim. It also violates the basis of logic (objective reality). So rational people must discard it.
So the objectively measurable conditions differ between them.