While we're at it, my personal peeve is hearing 999 out of 1,000 times people saying the "Democratic party," the "Democratic Governor," and " the Democratic position." It is my understanding that the correct name of that political party is "Democrat," hence none of the above should contain the trailing "ic."
I sometimes wonder if it is a "mistake" at all, since the left has consistently been pushing democratic ideals (in contrast to the ideals of a Constitutional Republic); the language has been distorted to the point that "democratic" now means "good, fair, equal" in many people's minds.
Democratic is the correct term when it’s used as an adjective, so the examples you cite are actually correct. The term Democrat is correctly used as a noun to describe a member of the party.
Republicans have been using the term Democrat as an adjective to purposely get their goat for more than 50 years. Apparently Democrats don’t like it.