They actually can do that as long as they claim it violates the federal constitution in some way. Suppose a state passes a referendum and amends the state constitution to allow slavery, or confiscation of your firearms, or changing the governorship into a dukedom and making it a hereditory office, or making Islam the state religion -- then would you complain that the judge found the amendment to the state constitution unconstitutional (under the federal constitution)?
Interesting thought. Of course, the hereditary monarchy thing wouldn't fly based on Article 4, Section 4 of the U.S. Constitution. I wonder how Article 4, Section 2, Clause 1 would play with the Fourteenth Amendment and the First, Second, and Thirteenth Amendments in regards to your other hypotheticals..?