The photons of electromagnetic radiation are chiral. And the reason is exactly the one you cite and which is also mentioned in the name - "electromagnetic" radiation. What's more, the photons of electrons all have the same arrangement of electric and magnetic field components. This is easy to prove.
In a radio wave, the electrons are moved back and forth on the antenna rod, emitting vast quantities of polarised photons. Their electric fields are sometimes orientated upwards (for a vertical rod, of course) and sometimes downwards every half period. At the same time, the magnetic fields of the photons are sometimes orientated to the left and sometimes to the right. If this were not the case, we would not be able to build a magnetic antenna as a receiver.
Addition
The electric and magnetic field components of an antenna are emitted perpendicular to each other. The two sketches show the near field of the antenna, in which the two components oscillate offset by 90° in the direction of radiation. It can be seen from the sketches that the position of the two fields can be readjusted according to the right-hand or left-hand rule (which also determines the chirality). Nature has - fortunately - decided that the electrons only emit photons according to the right-hand rule. Otherwise the generation of electricity and radio transmissions would be impossible. Lorentz force and Hall effects would also be impossible.
