At the risk of being a little annoying by challenging your premise rather than answering the question you've asked, the Republican Form of Government Clause - the only one in Article IV which touches on this topic - doesn't deal with entry into the Union. First and foremost, the clause simply doesn't expressly or clearly say anything about entry into the Union, and under well-established canons of interpretation, we have to assume that if they wanted to say that, they would have done so explicitly. Second, what it does say is that the federal government "shall guarantee to every State in this Union a Republican Form of Government"; the use of the phrase "State in this Union" heavily, if not exclusively, implies an existing state, such that the guarantee wouldn't apply to a polity or territory in the process of seeking to become a state. When this provision was discussed during the process of ratification, it was understood as empowering the federal government to block states from backsliding into monarchy or aristocracy. It arose again, more in the sense you have in mind, during Reconstruction, since the Southern states trying to get readmitted into the Union also barred huge swathes of their free population from voting. This demanded the question of whether such exclusionary systems could really be called "republican"; but even in that context, the issue wasn't really monarchies or legally-codified aristocracies being states, but insufficiently-democratic entities.

Source: Akhil Amar, America's Constitution: A Biography, pp. 276-81.