All observations of electromagnetic induction we have, are from the flow of electrons. The accelerated electrons in the antenna rod induce an EM wave with a right handed system of the electric field component, the magnetic field component and the direction of propagation:
Would an EM wave from positrons form a left handed system?
Edit: I have decided to reword this answer to explain more clearly where the source of confusion comes from.
Let's first understand what is meant by the right hand rule. It states, that the three arrows formed by the E-field, the B-field, and the direction of wave propogation must satisfy the right hand rule.
But why does it say that? The answer to that is quite deep and the root origin is the definition of the cross product itself. The standard textbook definition asks us to use the right hand rule to compute the cross product. You would then ask, does it not violate symmetry?
And the answer is no. Whenever you see cross product appear in physics, you'd always have a vector involved which cannot be directly measured without involving an observation that is itself defined by the cross product.
In case of magnetic fields, the observable is the acceleration on a charged particle that travels through the field. In the right hand rule system, if you observe that a positively charged particle travelling from the left of this screen to the right horizontally is deflected downwards then you will have to define the B-field as coming out of the screen towards you so that it satisfies the right hand rule. There is nothing sacred about this choice.
In a world where left handed things were preferred, you would have a left-hand rule system for cross products. But the physics will stay the same. The charge will still be deflected downwards. But you will now define the B-field as pointing inwards into the screen.
There is no meter in this world that would tell you for real if it is inward poining or outward poining vector field --for any such meter too will be built using this cross product convention.
Once you understand this, you will see why every right hand rule in electromagnetism is there. The Maxwell's equation involve the curl operator for magnetic fields and electric fields and that brings in the rule into the realm of changing fields too.
As another argument, consider the Maxwell's equations themselves. They hold regardless of how the fields are produced. There is no reference to the sign of the charge in the wave equation. And therefore, it will be theoretically impossible to influence the direction of the fields by just changing the sign of the charge.
No. The relationship between the direction of $\vec E$, the direction of $\vec B$, and the direction of the momentum of an electromagnetic wave is a property of the electromagnetic field, not of the source of the wave.
