In the end, to be fair, we measure both of them with photons (quite literally – GWs with laser interferometry and neutrinos by looking for Cherenkov flashes).
A fair point, but it should be said that a scale also only measures a some sort of an EM-based proxy for gravity, typically the compression of a spring either mechanically moving a needle or being electronically detected with strain gauges[1].
I guess my point was that when we peer to the skies and detect EM radiation at various bands, that's also just a proxy for something else that we're actually interested in. The photons aren't interesting in themselves, it's what we can infer about them by following the causal chain backwards. In that sense, it doesn't matter whether the photons are produced on Earth or a billion parsecs away.
It is useful to point out that everything we do is electronic in some way. All normal forces are really electronic forces. It just isn't the case that we can't observe forces other than EM, just that in the end everything has to become EM for us to be able to observe it, and... that's not too remarkable considering that we're made of electronic matter and are of such scales that nuclear forces are not relevant except in so far as they make chemistry possible.
