First I'm not aware of those sentiments in the 1860 Republican platform. I know that in political life, the other side demonizes their opponents' positions. But political polemics is not usually a rationale for rebellion/revolution/secession.
Secondly, if the Republican platform was so evil, why didn't the Southerners unite with Douglas to do everything possible to combat the mad tyrant Lincoln?
Lack of vision, I guess. Foolishness. A determination to have done with the North, before the North, swelling to unguessable dimensions with immigrant trolls, eventually bore down the South and crushed it despite anything Northern Democrats could do.
Possibly, the Southerners correctly read the political tea leaves, that the Republican and Abolitionist propaganda of sectional demonization had worked, and the North was now united as a politial monolith against the South. Under such circumstances, as Robert Rhett's circular appeal to the Southern States to join the secessionist movement and Robert Toombs's speech to the Georgia secession commission to the same end show, many Southerners felt that they could no longer save themselves from oppression by the North.