First, when the sexual revolution collides with the First Amendment, expect to see the First Amendment win. That’s the way the conflict played out in NIFLA and Masterpiece Cakeshop, to take the two most prominent examples from the Court’s most recent term. A more solidly originalist court would likely have decided Masterpiece Cakeshop on broader free-expression grounds, would scoff at the very notion that the government could revoke religious institutions’ tax exemptions for upholding their own notions of sexual morality, and may well take a dim view of efforts to prohibit counselors or pastors from sharing such notions with gay or transgender clients.
Second, look for the court to offer greater clarity on the Second Amendment. Since Heller and McDonald, the Court has essentially gone quiet about gun rights. Left undecided are questions about the extent of the right to bear arms outside the home (implicating carry permits) and the nature and type of weapons precisely protected. If an originalist court follows the late Antonin Scalia’s reasoning that the Second Amendment attaches to weapons “in common use for lawful purposes,” then broad “assault weapons” bans will likely fail.
Third, you’d likely find interesting majorities protecting civil liberties from police abuse.