Neither the Empire nor Federation is in a position to get uppity over State/Republic neutrality or at the very least less hostility.
Of course the Empire and the Federation are
exactly in the position to get 'uppity' over State/Republic neutrality. First, the State is supposed to be the
ally of the Empire while the same is true about the Republic and the Federation. Second, the State depends as much on the Empire as the Empire on the State. At least the same is true about how Republic and Federation relate to one another, if the Republic isn't depending more on the Federation than vice versa. Third, this means that if the State and Republic drop putting pressure on the enemy of their allies, those allies will put off pressure from their respective Enemy.
It isn't in the interest of the Caladri, though, that the pressure on the Gallente by the Empire is lowered, nor is it in the interest of the Republic that the Gallente press the Empire less. The benefit of any neutral stance would thus, best case, be canceled out, probably the allied forces would take steps that go a bit beyond canceling out any benefits - though not too bi, as to not overstep the room for maneuvering they have because forming even neutral relations is an
uncertainty as in a world with limited information available neither the State nor the Republic can be sure that the other party isn't playing a trick on them or will just outright block that move towards neutrality.
So if the Republic tries the "maybe we get it from our new friends in the State" move, the Gallente will be playing the "maybe we drop you like a hot potato" card and they will do so before the Republic can be even remotely sure about getting what they want from the State.
If you are allied with someone and you depend on that someone (and that's factually the case in the Republic/Federation and State/Empire cases, each party is depending on the other), than you don't make a move towards neutrality with the allied force's enemy.