Here, let me make it clear why direct democracy is a terrible idea for the US, based on my previous examples:
If we assume people would vote roughly equal to how they approved:
Interracial marriage would not have been legalized until around 1997. That's thirty years after it was actually legalized by the court system in the case Loving v. Virginia (against the, at the time, wishes of around 80-85% of the country.) And that's ignoring the fact that approval probably increased because it became normal as people legally wed, not in spite of it. It likely would've taken even longer otherwise.