It took us a day or so to get used to showing the "magic button" as we called it. Our trip was last month and this is how it worked for us.
Abigail was given a pink button at GKTW with her first name, city, state and the dates we were staying at GKTW. We also received a Guest Assistance Card (GAC) from WDW and Universal. Those cards were in a lanyard that you receive at the orientation at GKTW. The cards were dated and also had the number of people in our party....the WDW GAC had a green light stamped on it and said something to the effect of "expedite the guest's visit". I had never had any experience with a GAC before so I don't know what is normal.
Our first day at Magic Kingdom we did not do too many characters, but rode alot of rides. We would go up to the CM at the fast pass line and I would have Abigail in front and I would stand behind her with the lanyard on. Sometimes they would look at the card or button but the majority of time they did not. They just asked me how many people were in our party and allowed us right on through. For the rides that did not have a fast pass and did not have a CM at the very beginning of the line, I had to search a little bit and ask them what we needed to do. On Dumbo, we went through the handicap entrance. For the Alladin ride, we lined up at the exit. Most everything else we did had a fastpass line or a CM at the entrance and they would immediately show us where to go.
Never once did I feel like there were any guests that questioned our access to the rides and never did I feel like it was a burden to the CMs to ask questions. Everyone was very willing to help expedite our visit.
Our second day at Magic Kingdom, we were on a mission to meet all of the princesses (that was her wish....to meet the princesses and swim with a dolphin). That day at MK was by far our most magical day.....one that I know I will never forget. Our first stop was to the town hall where there are 3 princesses. The CM immediately saw her button and personally escorted us to the princesses. I can't remember the path we took, but it was never a "I'm walking ahead of everyone who has stood in line for an hour" type path. It was all very discreet. In the town hall, the line is such a way that you can't even see the princesses until it is your turn in the room, so no one would have seen us cutting in.
After she met (and spent some great quality time with) Belle, Aurora and Cinderella, we came out and Mary Poppins was outside. I could tell that the CM had cut the line off and was turning people away as we were walking by. We stopped just to ask a question and she asked if we wanted to meet Mary. Of course we did and again, Abigail was treated as if she were the only little girl in the park.
After we met Mary Poppins, there was a CM standing nearby and I asked her if she knew where we could meet all the princesses and she took my map of the park and drew out where every one would be that day. She also drew a map of how we should go and which one we should see first. It was such a simple thing but a great gift so we would not spend our time wandering.
At most of the character locations that were outside, we just went up to the exit and the CM would always notice us. Never did we have to walk through the line and blatantly cut in front of the other guests.
Part of the "once in a lifetime" opportunity of the trip is the "magic buton". Money can't buy what that button allowed us to do for that week. Before we went I was a little hesitant as well, but I am so glad that we took advantage of what it was meant for.
We were able to experience Disney in a way that most people do not know exists. (I know I've mainly focused on Disney, but Universal Studios was just as great...as well as Sea World.)
Maybe it was because the parks weren't very crowded while we were there and people weren't standing in insane lines (except for Toy Story Mania which is ALWAYS crowded....we rode it 3 times

), but I only heard a CM explaining to someone one time that we were with Make-a-Wish. It wasn't because the guest was upset, but just curious.
The one thing I kept in the back of my mind and explained to one of my son's when he said he felt a little guilty about going to the front of the line was that I'd gladly stand in line if it meant I had not had to wait in the hospital waiting room the nine times Abigail had surgery in the past 3 years. He understood and I don't think he felt guilty anymore.
I would encourage you to take full advantage of all of the perks of the button. It will make your trip more special and you will be able to do so many more things by not having to stand in the normal line. By the end of the trip, we were joking that we felt like the fast pass line was too slow and we wanted to skip it as well.