Now I will focus on the Left Wing version of academics. This is known by various names:
Generally speaking When W-T is used for Parshanut, i.e. to understand the original meaning of a given text, it can be seen as just another valid way of textual interpretation. It is engaging, interesting, and often enlightening
Almost ALL LW Orthodox that DO use Critical Method either explicitly or intuitively know to draw the line and do NOT apply it to Halachah l'Maaseh.
But many DO apply it to Halachah l'maaseh, and imho they are not really Orthodox anymore when they do that. They have traversed a boundary into the realm of Traditional Conservative [or perhaps into other "Liberal" streams"]
EG R Dr. MS Feldblum explicitly told me that his scientific techniques were NOT intended to undermine the "Shulchan Aruch" though many might actually use those techniques to undermine it
Similarly, Rav Dr. D W Halivni has made it a point to emphasize that we LEARN "Bet Shammai" even though it we do not follow his opinion, because it's still "Torah Lishmah" This means the same is true for RDWH's scientific method - it is Torah Lishmah, not geared for Halachic Revisionism.
Left Wing Orthodoxy since Hildesheimer-Berlin days have been OK with this system of academic theory so long as it was not applied to revise or to undermine Halachic Practice. OTOH, RSR Hirsch had his reservations and MOST of the Hareidi world condemned it entirely.
There are also several Flavours of Criticism
W/O going into details Lower Criticism addresses innocent scribal and printer's errors.
And there are two arenas for Criticism
2. Talmud or Torah SheB'al Peh [TSBP] in general
Few Orthos - if any - apply Higher Critical Methods to Tanach.
Lower Criticism has already been applied regularly to Talmud EG Hagahot haBach and Hagahot haGRA
Now the middle cases include R Feldblum and R Halivni who have applied Higher Methods to the Talmud, which has attracted much controversy
There are also Ortho Lower Critics Bible, we will set that topic aside for now.
Yet, AISI, if one draws the boundary and uses it for theoretical purposes it should be OK for Orthos to better understand Talmud via Critical Methods. There remains the risk of extrapolating and applying it to Tanach which could endanger "Emunah"