Light Ray

I think you are confusing electromegnetic waves with beams of electrons.
Other electromagmetic rays, radio, radar, microwaves etc behave similarly.
Beams of electrons or other charged particles will deflect in electrical or magnetic firlds.
Del

because they have zero rest mass. Why is salt not harmful to us, even though it is sodium and chlorine. The components of light are perfectly locked together, and are immune to the fields.

Kindly study Hubble telescope experiments to study Einstein's theory. Light beam gets deflected under gravitational forces of heavenly objects. For example Earth can behave like a heavenly lens (as per Einstein's theory deflecting Sun' s rays - may be seen from Pluto or beyond solar system.

May be if you have electric fields or magnetic fields like that in space - small deflections to light rays could be studied- till then it will be a academic questions and an academic answer.

Here's a somewhat simplistic answer, but it hits the key points of your question, I think:

The momentum of a photon depends only on its frequency (or wavelength) [E = hν]. To deflect a photon you'd have to change its momentum, which means your magnetic field would have to change the frequency or wavelength of the light.

On the other hand, the photon's spin angular momentum does not depend on frequency, so a magnetic field can affect the (circular) polarization of a beam of light.

Electromagnetic fields don't interact with each other directly but do interact with charged particles (matter) which can act as a intermediary. Thus you have electo-optical effects such as Pockels and Kerr effects.

EM wave is like a moving/changing/oscillating EM field with E&M fields perpendicular to each other. So when an EM wave encounters another E or M fileld, the interaction of fields modify the local field in the interacting volume/area.

so just to carry this a bit deeper...

Q: WHY does light bend when it enters materials with a different refractive index?
A: Because the speed of light is different in that Material.
Q: WHY is the speed of light different in materials with different refractive indices?
A: Because the atoms are closer together?
Q: If the light ray is interacting with atoms, how can it still continue in a straight line?
A: Because interactions with the atoms does not show unless the photon is absorbed. otherwise, it is the electric and magnetic fields that the photon is travelling in that are affected (compressed) by the atomic fields.

what?? that can't be right.. you are making that sh*t up...
okay fine, I am... but what else could it be? light is only composed of an electric and magnetic component... so both must be affected together to alter the apparent velocity... so somehow.. oh hell I don't know.

I have doubt about your first statement that light is fundamentally an electromagnetic wave. For example infra red light is a heat wave - not a electrostatic / electromagnetic wave !!! Light- visible / invisible etc etc - has been shown in a spectrum of wavelength - starting from near zero- then acoustic wave and then radio waves etc and then invisible and visible light and beyond. You also have acoustic waves - which definitely is not a EM wave !! Entire wave spectrum is NOT EM wave.

So first check your statement about light being a EM wave.

James Clerk Maxwell just rolled over in his grave.

Interaction of electric field that of photon is possible in medium at interfaces and only up to short distances.

Electromagnetic waves and even x-rays of high energies can bend in special conditions.

Don't expect them to bend using a magnet as wave is pure energy. You have to deform its field to interact with.