You are misinformed. Majority rule is only one part of democracy.
Another part is free and fair elections, which Jim Crow laws undermined.
Another part is the protection of the human rights of all citizens, which Jim Crow laws also undermined.
Source: Stanford University's Larry Diamond (book here, talk outline here)-- director of the Center on Democracy, Development, and the Rule of Law (CDDRL) and founding co-editor of the Journal of Democracy.