James Baldwin's open letter to Angela Davis contains the following sentence (emphasis added):
The will of the people, in America, has always been at the mercy of an ignorance not merely phenomenal, but sacred, and sacredly cultivated: the better to be used by a carnivorous economy which democratically slaughters and victimizes whites and blacks alike.
I've found two candidate definitions that might fit with the above usage of democratically.
1) Of a democracy (of a government by the people).
2) Relating to, appealing to, or available to the broad masses of the people.
I suspect Baldwin has in mind the first meaning; but, if so, I'm not sure how to make clear sense of that.