In particle physics, interaction with forces make roughly independent parameters. For example in a world with only electromagnetism, we would think neutrons were undetectable. The idea that there is a particle that only interactions gravitationally is hardly at odds with all of the other neutral particles we know.
Your point is correct, but the example is not good, because neutrons interact electromagnetically, due to having a non-null magnetic moment.
While the total electric charge of the quarks composing the neutron sums to 0, their movements are such that the magnetic effects do not sum to 0.
The particles that we know do not have a random collection of properties, they all belong to a consistent system.
For example in the set of 8 particles containing the 6 kinds of u and d quarks, the electron and the neutrino, the sum over the 8 particles of all the kinds of quantum numbers, e.g. spin, electric charge, color charge is null.
If some new particle interacting only gravitationally will be discovered, it will not fit in any way between the known particles so it must belong to some class of particles totally different from anything we know about until now.
Moreover, while it seems natural to assume that the dark matter if it exists must be composed of particles, like the matter we know, there is no evidence for this, so the dark matter might be some sort of continuous gravitational ether, for all we know.
I think you must have missed the conditional "would" in your parent comment's second sentence. Whatshisface was not writing about our world with our universe's physics. The "only" in his same second sentence is doing work there too, removing beta decay.
You could object that such a hypothetical world might not say something useful about our world, of course. I would not automatically agree with that assessment, however. It depends on whether "only" also ousts gravitation of free neutrons (or isotopes, if they exist in that world) or other means of testing the masses of bulk collections of matter with different neutron enrichment.
At the very least, we all seem to agree it was illustrative of a point about very weak interactions.
A gravity wave only interacts gravitionally right? And the energy it contains exerts a pull of its own? Say could you prevent one from escaping to infinity? Standing wave? Make it orbit something?
And I suppose even if it does escape to infinity it would be interesting to know if there is an analogue of the cosmic microwave background.
