Nevertheless, the method used by hyper-partisan AG Nessel to repeal a law she disliked (a collusive “settlement” with a convenient plaintiff) is repugnant to small-R republicanism as it has evolved in this country. The proper ways to repeal laws are through legislation (with or without the Governor’s cooperation), the State or Federal courts, or other methods set out in the State constitution (eg referenda).

Could a Federal Court invoke Article IV, Section 4, Clause 1 to “guarantee to every State … a Republican Form of Government” to set aside AG Nessel’s chicanery, and require her to get proper authority to modify the law?

I agree that it is problematic. Courts have been parsing campaign speech (and speech even more remote from eventual government action) for quite a long while, and the results have been the problems you describe and others too. For one thing, they incentivize litigants to search years’ worth of public discussion for the equivalent of thoughtless tweets, thus bringing to litigation the spirit of cancel culture.

Michigan’s attorney general had every right to campaign on her views about those who would discriminate against SSM. Personally, I think she was over the top, but if she has a beef with religion, so be it. I do not approve of federal judges acting like campaign speech policemen. They don’t have the expertise or the authority.