Thomas may not agree and I think his remarks suggest that he has the incorporation of the Second Amendment in mind as a guarantee of a personal RKBA.
If a government can violate unalienable rights, hasn't it become the tyrannical government that the Founders said the people had the right to overthrow?
What's stopping the formation of the Islamic Republic of New Jersey, for example, if the BOR are not applicable to the States?
Yes.
But regulating the RKBA is not "violating unalienable rights". To begin with, the RKBA is not an unalienable right. Second, even the 5th Circuit in Emerson said that reasonable regulations may exist. Third, the Founding Fathers voted against applying the BOR to the states when drafting that document, leaving the protection of those rights up to the individual states.
What if you lived in a state where the vast majority of the citizens did not want guns, and there was nothing in their state constitution protecting the RKBA. Over a period of many years, the state first banned machine guns, then rifles, then shotguns, and finally all guns.
Do you then have the right, nay the duty, to gather up all your friends and like minded citizens and overthrow the state government?
When it comes to Article IV, Section 4, that I quoted, the most logical answer from the context is that the executive branch bears primary responsibility for that. Look at the entire section: securing the states against invasion, assisting them in suppressing insurrections, etc. The clear context is that to "guarantee to each state a republican form of government" means to intervene in the event of a coup or a declaration of martial law, or something of that nature. Again, it does not mean micromanaging their laws and policies.
If a government can violate unalienable rights, hasn't it become the tyrannical government that the Founders said the people had the right to overthrow?
The Founders didn't say the people had a right to overthrow any government which happened to violate their rights at all (since no government could be held to such a standard of perfection at all times), but "when a long train of abuses and usurpations...evinces a design to reduce them under absolute tyranny". Either way, however, if it gets to the point where the people of a state have a right to overthrow their government, that still doesn't mean that the federal judiciary needs to get involved.
What's stopping the formation of the Islamic Republic of New Jersey, for example, if the BOR are not applicable to the States?
Notwithstanding the fact that a demented application of the Bill of Rights to New Jersey is currently facilitating (at least indirectly) exactly what you describe, what can stop it is the New Jersey constitution, the voters, and (as you suggested in another post) civil disobedience, and ultimately stronger measures if they become necessary.