On this topic, I’ll for now just quote from the critique made by liberal law professor Rick Hasen:
Judge Kavanaugh is no moderate…. On the campaign finance point, let’s not forget that Judge Kavanaugh was the author of Bluman v. FEC, the case that upheld the ban on foreign spending in elections. While that might look like a ruling against deregulation, in fact it is not. Indeed, I believe that a Justice Kavanaugh could well vote with a new SCOTUS majority to hold that laws effectively limiting foreign influence in our elections violate the First Amendment….
As for RNC v. DNC, that was a case on contribution limits where J. Kavanaugh was bound by Supreme Court precedent, and tells us very little about where he would be as a Justice of the Supreme Court.
Having read Bluman and studied J. Kavanaugh’s writings in this and related areas, to me the only question is whether he’d be more like Justice Scalia (voting to strike down more and more campaign limits) or like Justice Thomas (voting to do that AND strike down campaign finance disclosure laws).