I never had an issue receiving a card or using the card for my autistic daughter (who is turning 18 this year). We've been three times (last three years), and have been treated really well by cast members and characters (especially the characters!!).
There have been times when it took longer to get into a ride (Pirates of the caribbean) than if we stood in lines, but considering our daughter's abhorrence towards crowds, it did not matter. With Pirates, we got to sit in the shade away from the crowds, chat about what she had done so far, and had room for her to walk around when she needed to (without bumping into others).
I know this really doesn't need to be said for 99% of us, but the GAC card isn't intended to expedite rides, but provide accommodations for those with special needs. In fact, there have been times we were allowed into a (longer than normal) fastpass line where we had to leave before getting on the ride, because it wasn't quite what our daughter needed at the time.
Another thing we found last trip is that if the wait time was less than 30 minutes on a ride, we were told we needed to use the regular line. In this one case, we explained that our daughter couldn't handle it, and the cast member understood... in that case, we stood by the handicap entrance until it was our turn (as if we had stood in line). So even in cases where alternative entrances don't expedite getting onto a ride, the cast members still worked with us so that our daughter had what she needed at the time (lack of crowds).