As has already been said, reading that and concluding that she's arguing that objectivity does not (or cannot) exist is bordering on a deliberate misinterpretation of what she said. Sorry, but it's just dumb. Even the civilians commenting on Chait's tweet recognize how dumb that claim is
Other obnoxious things about this (from both "sides"):
(1) What MR is saying is FAR from anything new. If anything, it's platitudinous, a very old saw, and gussied up to look more timely or interesting than it is. It's an expansive road which nearly everyone recognizes the existence and legitimacy of, but which for decades, has led to nowhere.
(2) The claim that this is "getting worse" is equally inane. This implicit division in the discipline has been expressed this way for nearly a half century now, and it's not getting even remotely worse. Instead, it is much, much, much better than it was in the 80s and 90s (you'd have to go back that far to actually find anyone that anybody has ever listened to who argued that objective reality and facts aren't real). The MRs and KWs of the late 80s early 90s very well might have actually been taking the extreme positions that are now falsely being attributed to them as people talk past each other. That doesn't really happen anymore, and as I personally fall on the KW side of these things, I find it incredibly obnoxious that she seems to be deliberately misreading MR so that she can dress up for some dumb Civil War reenactment she wants to fight.
3) It is as it has always been: 90% of practicing sociologists are just doing their work, and generally disinterested as to where other people fall WRT to activism and advocacy. They also recognize this "justice" vs. "empiricism" nonsense as the canard that it is, and are too busy working to even really care about it. Meanwhile, 5% of the discipline on either side is rooting for (and sometimes actively trying to create) group polarization because that's where they draw their intellectual identity from. Both of these sides suck. They both want a fight that nobody else has time for or is interested in.
4) I think a mistake a grad student could reasonably make on this stuff would be to confuse loud voices with representative voices. They're not. Groll is an outlier (more generally) just as much as KW is an outlier on this one. The vast majority of practicing sociologists seriously care about none of this, which is why they're doing what they've done for decades: ignoring it and paying attention to more important things while the small cadres of people who draw their identities from this stuff occasionally fling sh!t at each other.