When I was a Democrat activist, I always said “Democrat party”, not “Democratic party” because when I first became a party worker, the old timers told me that’s how it was. The notion, as I recall it, was that the party was an otherwise non-homogenous group of fiercely independent-minded people who basically thought alike on some things but not all. “Democratic party” they maintained sounded too much like a herd with a herd mentality. Whether it did or not, that’s the way it was put to me.
So I still sometimes say it around here, more to honor those old party people, most of whom are no longer alive on this earth. But in other places people take offense. I have been made aware of other places where it was the same.