My understanding is that Kavanaugh has so far been more liberal than expected. Obviously it's early days but it seems highly unlikely that he's going to be the next Clarence Thomas which is what the left/right feared/hoped he would be.
Actually here's a graph that pretty much shows this:
As can bee seen from the above most justices tend to become more liberal with time. The theory is that they move to Washington D.C. for the job and end up moving in social circles that are more liberal than where they came from which influences their way of seeing the world.
Clarence Thomas is an obvious exception to this. His wife is a signed up MAGA devotee and apparently he records Rush Limbaugh's show every day so that he can listen to it.