The granite tops will supported solely by the sides of the cabinet, anything that is over the toespace, therefore your center stile is not structural, at least as far as the countertop is concerned. If a countertop installer tries to shim an installation at the center of the cabinet, I am sorry to say they would be doing it wrong. It must be shimmed at the sides of the carcass. The sides of the cabinet that go straight to the floor is where the structure is.
Although it is not needed for support of the countertop, it is needed for the support of the drawers and possibly the interior shelf. The structure of the face frame in the third picture shows the rail at the underside of the drawers is cut to either side of the stile you wish to cut out. When it is gone the only continuous part that will support the drawers is the upper rail under the counter. You could add another header, so to speak to take up support for the drawers.
One thing I think I see in your picture is that the left side of the cabinet looks like it has a toespace that turns the corner, so in essence, that cabinet side is not structural either. It looks like it is the last cabinet in that run, so the countertop installer may need to give some thought on how the top will work on that side.