We go to Mary Queen of the Universe Shrine every time we visit wdw, which is about 3-4 times a year. I've never really felt pressured for donations at all at any time during the mass (no more than any other mass anywhere). This shrine was built from tourist's collections, it has no parish like a regular church and is run by volunteers. It is a beautiful church, a real attraction to visit in and of itself and well worth a few minutes ride since it is very close to disney property. It's always interesting to see where everyone is from before mass gets started. They have a great gift shop and the prices are so reasonable; you can get religious medals, statues, cards, etc. A little further down the road are the outlets, including the disney outlet, usually you can get some great deals there.
I really do miss the masses at the Poly though. Not just for the convenience. It was nice to have mass outside and the homily was always so good (priests were from mary queen of the universe shrine). They even had the live music accompaniment. We were very sad to see this go away but now enjoy visiting the Shrine.
Btw, taxis will pick you up from any disney resort. Not sure of the cost since we usually have a car.