If the US cannot interfere in any state without approval of its legislature or executive, how then can it guarantee each state a republican form of government? That would seem to require, by definition, the federal government being able to override a state government that attempted to set up a monarchy or oligarchy.
The part about application of the legislature or executive, is related to domestic violence within the state, not to the preceding clauses about guaranteeing a republican form of government, or protecting against invasion.
The invaded state, instead of relying merely on its own strength for defence, and instead of gratifying its revenge by retaliation, may prudently call for and gratefully receive the strong arm of the Union to repel the invasion, and reduce the combatants to the equal level of suitors in the high tribunal provided for them. In this course, the political estimation of neither state could receive any degradation.
William Rawle
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The purpose of the protection against invasion provision was primarily to insure the federal government would protect all the States equally in the event if invasion. Too bad there are no Constitutional instructions about what to do when the 'protector' is the one doing the invading.
The possibility of an undue partiality in the federal government in affording it's protection to one part of the union in preference to another, which may be invaded at the same time, seems to be provided against, by that part of this clause which guarantees such protection to each of them. So that every state which may be invaded must be protected by the united force of the confederacy.
St. George Tucker
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Since all the States all have the Republican form guaranteed in their respective Constitutions, I find the conjecture that they would attempt to set up a monarchy or oligarchy both ridiculous and nonproductive.