This case intersects with other areas they have an interest in?
Yup. This is the first one where registration was implicit, or country wide "approval" was proposed for a fundamental right. They see it easily transitioning (as we all have been screaming) to other rights (speech, assembly, due process, search/seizure, voting, etc) that the gov sees as "given" to the public, rather than already existing.
Effectively, requiring a purchase (background check fee) to exercise a right finally made someone have the thought process of...wait...isn't this like a poll tax?