I would donate to ANOTHER (secular) cause, like the American Cancer Society, and send a nice sympathy note to the person whose father died. I do not think it is appropriate, mipnei darchei sholom or not, to donate money (to any organzation) that will potentially be used by ovdei A”Z. We cannot unknowingly contribute to someone’s A”Z, which is one of the 7 Mitzvos of Bnei Noach, so they as well as we, are chayav in it.
If it were anything OTHER than A”Z, it would be a lesser issued, but A”Z is a special catergory, in that even THINKING about committing it is a terrible aveira. I think this is an area in which we need to be really careful.
I would have said, “I am so sorry for (so and so’s) loss. I absolutely want to show respect for him by contributing to charity in memory of the departed. However, fopr personal reasons I cannot contribute to this particular organization, but would be very happy to contribute to another one in his name. Perhaps you know of another one that would be meaningful to So and So.”