I always give to the Eastern Paralyzed Vets of America. I guess they changed their name to United Spinal Association. They always send assorted Christmas cards and address labels at Christmas. Some say "Merry Christmas, Seasons Greetings, or Happy Holidays." Now if they only said "Happy Holidays" I wouldn't like it, but it doesn't seem like they are trying to be politically correct. The items they send are always beautiful and I'm glad to donate to an organization that helps our vets. In fact, one of my professors at college was a paralyzed vet who was given his wheelchair from this organization. That's another reason I donate. I saw how they used their funds.
I'm not sure about this other organization you mentioned. Maybe you could write and ask them their Holiday/Christmas policy. They might even send you information about how they spend the donations. I'm all for helping our vets.