Interesting points. I was thinking, we're generally treating EM fields like they're unaffected by gravity, because we've measured the field strength around a magnet and saw that it wasn't drooping to the ground.
But I guess, the influence of gravity is so weak on EM fields, that it only becomes apparent near a black hole and therefore, it's hardly possible to actually measure a deformation on Earth. And therefore, we just don't know.

Plus, of course, other reality-bending stuff, like the EM-waves we use while measuring (e.g. visible light) being affected by the gravitational pull.

Do you know, if there's anything for which we've secured that it's unaffected by gravity?
Apparently, there's a few particles/field-peaks/whatever, which are deemed massless, but given that no mass does not mean unaffected by gravity, that's kind of moot...