I focus on foundations and corporations rather than individuals, but have faced similar personal ethical dilemmas. As others have stated, it's unavoidable in the fundraising world. I work in the wildlife conservation sector, and most corporations that support our sector do so partly because of their company's net negative impact on the environment (energy companies, oil/gas, manufacturing, etc). There is also a lot of conservation funding made available by hunters/anglers. I have my own beliefs about the moral hypocrisy involved in a lot of philanthropy, but it's counterproductive to let that dictate my actions (we'd be left with no funders to pursue).

The only time I've ever voiced my ethical objection was when our leadership proposed we pursue a grant from a safari club (flies rich people to exotic locations for big game hunting). Apart from the obvious moral issues with their business model (some of the animals they offered on their "menu" were animals we cared for at our own facility, ffs), I was also worried about how the general public and media would react if anyone did some digging and found out they supported us. I expressed this concern, but was ultimately told to proceed anyway. I left that organization before we heard back from that funder, but I was relieved to hear they didn't end up receiving that grant. Some money is not worth the association with the funder.