Because citizens of the United States were being denied rights held by their fellow countryman on account of their skin colour.
That is unjust.
To play some devil's advocate, why is the relation between two men in Missouri the concern of a man in New York?
And what makes it more significant to a New Yorker than the relation between two men in Nigeria?
By a very stripped down super doctrinal libertarian outlook, if the terms of employment is between the employer and employee are a personal matter between the two, to be worked out by them, why is the relationship between the black Misourian people and the white Misourian people a private matter to be worked out by the involved parties?
Obviously, almost no libertarian sees things that way. Some may be comfortable with indeviduals behaving out of line with their principles, often unstate, but very few are comfortable with groups. Thus so many high level globalist libertarians.
I think it's these unstated but firmly believed premises that cause libertarianism as a movement so.much trouble.
After all, even you above de facto have came out in support that it was New York's duty to micromanage social relations in Misouri. Having demanded that New York do so, what grounds do you have to critize New York for doing so?
That above is more or less what i mean by the next logical step. Though admittedly its a different framing than one normally considers thing, though not i think an invalid one.