DY, to answer your question. It’s not so pashut. If someone were to come to me as a school or a shul and make this offer: if I become mechalel shabbos, I’ll donate 20% of my profits, I would try to deter him from being mechalel shabbos. If I couldn’t, I certainly would not accept any donations.
However, what if the person was never shomer shabbos and his money was earned legitimately and honestly? I would agree with newbee that in this case I would accept a donation in that at least the money was being put to tzedakas. The yeshiva in Las Vegas has nearly 300 students in a beautiful building entirely paid for by Adelson. Without his money, these kids would be in public school. Better a yeshiva than donating money to Harvard or a museum.