When I was trying to earn my high school diploma I took five online high school courses from BYU independent study. BYU is a Mormon university, which I believe is funded by the Mormon church. Was it wrong for me to take these courses? Would it be considered supporting the Mormon church? Also could the principal of abstaining from things polluted by idols be applied to this? I knew another girl from church who also took BYU courses, but her father didn't think it was wrong. If it is wrong should I still use my diploma to get a job since I earned it by taking those courses? I don't want to earn anything by sin.
The rule is similar to the ones discussed in the New Testament about the eating of meat. Paul argued that meat is meat, and it doesn't matter where it originated. "Eat whatever is sold in the meat market, asking no questions for conscience' sake; for "the earth is the LORD'S, and all its fullness"" (I Corinthians 10:25-26). In the truest sense, your family purchased a service that was offered by a university connected to the Mormon church. Your courses did not support Mormonism, nor did it connect you as a supporter of Mormonism. It is just like others who take classes at universities associated with some denomination (and there are a lot of them out there).
I might buy a dinner at a restaurant whose owners contribute to a denomination. That is their choice, but my choice was to buy a dinner. Now, I wouldn't go to a denomination to buy doughnuts and coffee from their shop -- that would be seen as directly supporting the denomination. However, to purchase a produce at a place that is only loosely connected to some denomination is not wrong because it doesn't connect you to their teachings.