The GAC is designed for people with "invisible" disabilities (those not related to stamina and/or mobility). They are issued by Guest Relations based on the needs of the person so they will, as much as possible, be able to enjoy attractions as would a person without the disability.
They are not, and it so states on them, intended to be allowed to bypass lines. Usually it will involve a special waiting area or special seating.
There are special GACs which do allow bypassing lines, but these are issued only to families with children who are here as part of a Wish Trip. If your family does not have a child with terminal or severe disabilities you do not get (or want) one of them.