For the past few years I have been reading the top two conservative magazines, National Review and The Weekly Standard, in an attempt to understand how the conservative mind works. One thing which stands out is that the word "conservative" means many things to different people, and it certainly is not a monolithic movement, just as Communism was not during the cold War.
Certainly we know from past experiences that the direction a Supreme Court nominee takes once confirmed cannot be predicted with any accuracy. One of the reasons that this will, I think, be the case with Kavanaugh is that applying conservative principles to Supreme Court decision-making is especially haphazard.
For example, take the Roe v. Wade decision. Many who oppose Kavanaugh are fearful he would vote to overturn this precedent. I say the fears of this are overblown. One reason is that a true conservative respects precedent, and tends to dislike change. As a principled conservative, Kavanaugh will, I believe, have a healthy respect for precedent.
And then there is the further point that the true conservative is one who opposes the intrusion of government into the personal lives of its citizens. Hence, the true conservative would feel that government has no business making reproductive decisions for its female citizens. Those who advocate for governmental intrusion into the private lives of its citizens, as in dictating who we are permitted to marry, etc., usually call themselves conservatives, but in reality they are liberals because they are advocating for greater governmental control.
Other important areas on which there is much disagreement among conservatives include the scope of executive power, the scope of agency regulation of our lives, and how much deference to be shown to the states.