> Assuming that the magnet and EM waves were very strong, could we (in principle) observe that magnet being pushed towards / away from the radio signal source?

You would need radio waves with impractically low frequencies (and therefore impractically large antennas).

> And do radio waves have some kind of stronger effect on molecules that are dipolar?

Radio waves interact very well with metal, which is not dipolar. If you want to poke around at dipole moments with EM radiation, you're more likely to do it in the IR region, from what I remember from my instrumentation class in chemistry.

EM fields interact with substances because the EM field can be absorbed and make electrons or other charges in the substance move around. Different types of motion require different amounts of energy, and this puts them at different places in the EM spectrum.

In the middle of the EM spectrum you can excite a lot of various vibrational modes. With longer wavelengths, you can interact with things like unpaired electrons. With short wavelengths, you can interact with electrons deep inside a substance. Each different part of the EM spectrum lets you probe a different aspect of the substance you're testing... in one part of the spectrum you might be able to see resonant peaks corresponding to specific structures or shapes, in another part of the spectrum you can see peaks corresponding to specific elements.

Take what I'm saying with a grain of salt because this is all half-remembered from chemistry classes a long, long time ago.

> ...effect on molecules that are dipolar?

That's exactly what happens in a microwave oven. Water molecules are dipolar and vibrates with the microwaves.

I thought microwave heating had more to do with inducing electric currents in the water and the resistance losses heating the food?

That being why they’re bad at defrosting ice unless there’s already some liquid water present, and why they can heat molten glass but not (directly) melt solid glass?

(I’m neither a chemist nor a physicist nor a radio frequency electronics engineer, so I may be way off here).

"Dipole rotation is the mechanism normally referred to as dielectric heating, and is most widely observable in the microwave oven where it operates most effectively on liquid water, and also, but much less so, on fats and sugars.":

https://en.m.wikipedia.org/wiki/Dielectric_heating

In ice the molecules are not free to rotate as they are in liquid water.