It's been a while since I posted, so it may be wise to start by affirming my agreement.

I do think it gives us talking points as a nation and then as Christians that merit thorough discussion. In looking around on a few sites that largely reflect liberal Atheist and conservative Christian viewpoints there can be little doubt that liberals oppose Judge Kavanaugh's confirmation sincerely and ardently enough for some to even propose and encourage violence in championing their agenda, and conservatives support Judge Kavanaugh's confirmation sincerely and ardently enough for some to even champion his confirmation were Dr. Blasey Ford's allegations true (though of this “some” sample there's a distinguishing between characterising the alleged behaviour as attempted rape and manslaughter, or viewing them as druken high-school campy horseplay). Those are the extremes. The question then becomes that for folk between those extremes, to what degree ought a SCOTUS nominee's personal and professional histories be determinant of both their worthiness to represent all the people of the nation and to do so with a moral clarity and comportment reflective of national expectation.

What I've heard from liberals is that Judge Kavanaugh is “evil” and evil ought to be eradicated and especially precluded from the SCOTUS – that having this evil on the Court will do irreparable harm to the nation. And, in any case, that Judge Kavanaugh cannot possibly represent them with any degree of fairness or non-partisan justice.

What I've heard from conservatives is more of a mixed bag, but on the guilt/innocence issue those believing Judge Kavanaugh largely claim his innocence establishes his moral worthiness to the Court, and his record in jurisprudence establishes his fairness in representing all the people of our nation.

However, among conservatives there seems also to be a noticeable group of folk giving a heavy ponder to this last part of the hearing and accentuated claims from others earlier regarding Judge Kavanaugh's temperament and seemingly partisan remarks directed to the Democrats. This speaks to what the OP reflects on the linked article.
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Douthat makes the case that it doesn’t really matter whether Judge Brett Kavanaugh is guilty or innocent of the allegations against him. Even if Kavanaugh is innocent, he has been tainted by accusations made against him and on those grounds alone could be unfit to serve on the Supreme Court.

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Even if Kavanaugh is innocent of the charge of a teenage sexual assault… to give such prominence and power to a man credibly accused would both leave an unnecessary taint on his future rulings (especially given his appointment by our Playboy president) and alienate social conservatives from the persuadable Americans, women especially, whose support any pro-life program ultimately requires

It's striking to me just how much the current debacle reflects that of the confirmation of Justice Clarence Thomas to the SCOTUS. While Democrat Sen. And Committee Chairman Joe Biden opposed and voted against Justice Thomas on policy, other Democrats indeed expressed that Justice Thomas would be too tainted by allegations of sexual misconduct to effectively serve on the Court.

I heartily agree that mere allegations ought in no way influence or effect appropriateness to serve or effectiveness of performance. Further, while I would personally be uncomfortable with a drunk or lush or alcoholic on the bench, and equally uncomfortable with someone who may have done something somewhere in high-school or college that was sexually inappropriate, those demographics represent a very large segment of the American people and American culture. To me, inappropriate juvenile behaviour is not and should not be an automatic disqualification, even to the highest court of the land. The “casting stones” wisdom remains, even considering King David's record of adultery, murder, and redemptive restoration. Did King David remain in struggle with the consequences of his repented actions? Yes, he did. Did they remove or disqualify him from service? No, they did not, not with repentance.

I realise too, the angle toward just picking some other unstained nominee out of the bag, but hey, this has become the new normal – delay and destroy the competition by any means necessary. That sort of strategy ought never be rewarded, whether of Democrats or Republicans. We shouldn't as a nation or as Christians be looking for ways to enact treason against our President, even if or when we think it's in our nation's best interests. It's maybe too modern and common a phrase to sink in for some, but, "One nation, under God. with liberty and justice for all" is something to which I think Judge Kavanaugh remains steadfastly committed.

In college we studied Richard Niebuhr's 5 classic Christian Christ-culture options trying to untangle messy debates on living in the world. The thought proposed by Douthat is that in saving a persuadable culture toward Christian value(s) we ought not to needlessly confront them directly with pure contrast and certainly not belligerently in stark prior distance from agreement and acceptability with them. Christ though, calls us to be salt and light, a preserving beacon of hope toward redemption. While it's most certainly true that God came to Earth and tabernacled among us as one of us, it's equally true that He did not compromise nor withdraw His service from being thought either a prude or a fraud. That He was tainted by false allegations thankfully did not dissuade Him from all needed loving service on our behalf. Neither ought such challenge dissuade or disqualify Judge Kavanaugh.