In reality, Kavanaugh was picked by Leonard Leo, the executive vice president of the ultra-conservative Federalist Society. Leo has picked the last four Republican-nominated justices on the Supreme Court as well as dozens of federal judges on both the trial and appellate benches nominated by Republican Presidents (details here).
Kavanaugh's record on LGBT rights is thin, but he's a card-carrying garden variety religious conservative, so we have to expect he will not protect our rights like Justice Kennedy did. He will side with religion over LGBT rights and government domination over LGBT privacy.
The Daily Beast recently published an article (link here) on five important LGBT rights cases that may be impacted by Kavanaugh taking a seat on the high court, which looks very likely at this point. Watching cases like this will help to determine where the high court is going and which of our rights are being chipped away.
I wish I could be more positive about this development, but there's probably no silver lining to this dark cloud. My only recommendation would be and I've made it before: think about moving to a so-called "blue state" where LGBT rights are protected under state constitutions and/or state laws.
Most people agree that California is the most LGBT-friendly state in the country (details here). Having lived primarily in Los Angeles since 1985, I concur.