Justice-designate Kavanaugh is a textualist who believes that the wording of a statute or of a section of the Constitution, as well as the intent of those who wrote it. should be the determining factors in its interpretation. But he is also a believer in the principle of stare decisis ("it stands decided"), meaning that he tends to feel bound by precedent and does not lightly support the overturning of decisions already rendered or principles already established. He is seen as somewhat less of a hard-liner on abortion than some conservatives might like and is an open admirer of the man who appointed him to the Federal bench, George W. Bush. His ties to the "establishment," as well as his role in preparing the way for the ultimate decision that the insurance mandate of the Affordable Care Act was a tax and thus constitutional, put him in the doghouse of many conservatives. All-in-all, he is a cautious, scholarly man who has emphasized in his speeches and writings the necessity for judges to leave partisanship at the door of their chambers and be honest, conscientious "umpires." Some conservatives are apprehensive; some liberals are actually relieved at the appointment of Kavanaugh, whom everyone agrees is a remarkably well-qualified choice. While I have no doubt that every Democrat in the Senate will vote against him, they will have no reasonable cause to do so. He is a cautious, scholarly man of conservative instincts with a great respect for precedent and a firm conviction that judges need to be above ideological politics and decide cases on their merits.
So what will happen now? My guess is that the states will eventually be allowed to restrict, but not outlaw, abortion. Obergefell vs. Hodges may be modified, perhaps allowing states to limit marriage as such to heterosexual couples as long as equal rights for gay and lesbian couples are also legally guaranteed. I doubt that many will do so. I think it's a good bet that bakers or florists who believe that they, themselves, would be sinning by baking a cake or providing flowers for a gay "wedding" will be protected from legal reprisals, but not those who refuse merely to show their disapproval of same-sex "marriages."
Otherwise, I don't think much will actually change. Chief Justice Roberts will probably now become the "swing" vote on a Court which will definitely be more conservative than it has been for a long time, but actually more centrist than conservative. The sky will not fall on liberals, though the petty partisan sniping has already begun in the leftist media, and while conservatives may not find in Judge Kavanaugh someone who agrees with them on every point, they will find him to be someone who speaks the same language they do.
As I've said before, I believe that Judge Kavanaugh will be narrowly confirmed- and be the last conservative judge appointed to the Court and confirmed by the Senate in my lifetime. Ross Douthat points out that it would take a sixth and perhaps even a seventh conservative justice to make the Court as conservative as it has been liberal in recent years. That won't happen. I expect the Democrats to gain control of the Senate this fall, to win the White House back in 2020, and to retain it indefinitely. The price of winning the battle to get Justice Gorsuch and Judge Kavanaugh on the Court by electing Donald Trump will, I continue to believe, in the long run, be losing the war by letting the Democrats replace Ginsberg and Breyer and every other justice who vacates his or her seat for a very long time. The Republican party as we have known it is dead and a very different animal has taken its place, one which will have a very difficult time assembling the coalition which narrowly won Donald Trump an Electoral College majority while losing the popular vote in 2016 in the future.
But as one who wants to be absolutely fair to a president whom I hold in personal contempt, the nomination of Judge Kavanaugh, like that of Justice Gorsuch, is an excellent one, and a savvier one than I would have expected from him. Give the man his due. The country is better off because (unless Susan Collins or Lisa Murkowski rebels) Brett Kavanaugh will be on the Supreme Court.