My experience includes being interviewed for a colleague's DoD clearance. They do want to know about adverse information such as DUI / alcohol abuse. As I understand it, the recent background investigation interviews for Judge Kavanaugh are not available to the public. Is at least one purpose of the judge's background investigation to determine if there is a drinking issue (that would be in-scope any DoD investigation)?
Kavanaugh has had two of the DoD background investigations at least, as they are required to get Yankee White clearance, which allows routine access to the President (He had two such investigations during George W. Bush's presidency). So the issue would have come up then at least, if not sooner. The reasons they look at alcohol abuse is that, as the DoD says, Loose Lips Sink Ships, and as the Romans observed In Vino Veritas (In wine, there is truth). They also look into it for matters as an substance abuse issue could be exploited by an adversary or could lead to poor choices.
Typically, these investigations are lenient on youthful indiscretion during college and high school, as it would be near impossible to find a new recruit who hasn't drank under-age during college. It's quite common. Additionally, the scope of these investigations is 10 years or to your 18th birthday, which ever is sooner. If Kavanaugh was 17 in 1982, than it would not be covered in a 2001 investigation. They also require that you list six separate non-familial witnesses, with four of them being able to vouch for you during the entire portion of the scope's time AND they cannot be family members. Kavanaugh's first background check was when he clerked for the Solicitor General of the United States, in 1990 or 1991 (cannot remember the specific date, but it was early) so his college years could have been investigated during that time, though I do not know what the DOJ process is.
Drinking is not in and of itself enough to get you disqualified, but does need to be assessed with other issues to make a determination on if the subject of an investigation could be trusted to handle classified materials. As it's not an illegal substance, they are looking for a problematic pattern, not if the subject drank underage, even if it was a glass of wine at Christmas Dinner.
It should be stressed, that this is a very, very, through screening. As one DoD hiring manager I know personally has told me, the general rule for hiring for hiring for a position is that for one billet that needs to be filled, give a conditional job offer to 4 people. This is due to the fact that, because of the rigorous nature of the background checks, only one person is likely to clear them. Basically, the FBI is not dropping the ball on this matter.
Supreme Court justices are nominated and confirmed by rules in the Constitution. The President nominates, and the Senate confirms by majority vote. There are no other legal requirements, just what the President and the Senate require, and in this case the majority of the Senate appears to think in-depth investigation is unnecessary.
There is no Constitutional process for hiring someone for the Department of Defense (indeed, there is no Constitutional requirement to have any such department), so it's a matter of Federal statute and DoD policy.
So, the rules are very different.