Democracy does not imply that a political party cannot be banned. Nazi party is forbidden in many countries that are usually considered democratic or at least flawed democratic (democratic formally, but not in effect).

Democracy in contemporary context also does not mean direct democracy, it means representative democracy. That's why banning a party that has overwhelming popular support can still be democratic, if it is done lawfully by democratically controlled institutions (via regular and free elections). Dissent of the people for a specific decision or policy does not have legal power in standard democracies unless a special mechanism is invoked, such as referendum with the power of law (whose invocation the president or representatives have to agree on, details depend on country).