A changing magnetic field will always induce an electrical field and vice-versa. Even just moving a magnet with your hand will generate an electrical field. Near-field effects of an antenna still involve this interaction.

The key to the resistance of very long wavelengths of EM radiation (or equivalently, very slowly varying electric/magnetic fields) to attenuation when traveling through a metal is the nature of the way metals expel electric fields (they don’t generally block magnetic fields). When you apply a static electric field to a thin conductor, electrons will be pulled away from one side and toward the other such that the field inside is zero. However this migration of charges will actually result in the electric field on the far side of the metal being nearly the same as the field on the side closer to the source!

If the wavelength of some EM radiation is much longer than a metal obstacle is thick, the fact that the electric field is excluded from the interior of the metal won’t matter much. Even if the metal wasn’t there, the electric field strength wouldn’t vary much over that distance, and on the other side of the metal the induced charges will restore the roughly “correct” field. Since the magnetic component won’t vary much over that distance either, the fact that there’s no varying electric field inside the conductor to reinforce the magnetic field won’t significantly attenuate it.

If you’re familiar with Faraday cages, this will sound all wrong. Isn’t it long wavelengths they can block, and short wavelengths they can’t? This true when dealing with EM radiation in the “normal” radio bands and higher, but it turns out their ability to attenuate radiation falls off in the other direction too (once wavelengths get extremely long). When dealing with EM properties of materials, there are a huge number of different effects that apply in different circumstances, and it’s easy to forget one and confuse yourself.