The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
The government of the United States - the federal government - can and should protect each of the states in the union from invasion and domestic violence but cannot "guarantee a Republican Form of Government". There is simply no mechanism in the structure of the relationship between the federal government and the government of each state that would make it possible to do that.
If someone attempted to establish some other form of government - a dictatorship, monarchy, or theocracy, the federal government could send troops in response. But within a framework with a system of representation , elections, and voting, determining that the government of a state is not a "republican form of government" because it fails to give all citizens equal representation and does not ensure majority rule, is a very subjective matter.
The argument could, and should, be made that none of our fifty state government are true democracies. It will be up to the citizens of each of the fifty states to decide whether the government of their state is a republican form of government or not and to enact the reforms necessary to make the government of their state a true democracy if they want a republican form of government. To paraphrase "Fighting Bob" LaFollette: If the people of a state want a republican form of government, they must do the work of establishing a republican form of government.
There is no state in the Union that currently ensures truly equal representation for all of its citizens. As is the case with the federal government, putting a system of proxies for citizens and weighted votes for legislators in place is the first reform that needs to be enacted in every state.
Some states already have provisions in their constitutions that allow amendments to be proposed by a simple majority of legislators and ratified by a simple majority of voters. Those that don't should amend their constitutions to put such a system in place.
Every state currently allows their governor to veto legislation and requires a super-majority in the legislature to override the governor's veto. This is a reform that may cause some consternation and require some discussion. But John Locke was right. The legislature should be supreme. When a governor can veto legislation, the legislature is not supreme. The citizens of each state be able to vote on whether or not to retain the veto power of the governor. The citizens of each state be able to vote on whether or not they want a republican form of government - a true democracy - perhaps even a perfect democracy.