Ave María,

Who are some of those trad clerics who believe in BOD only for unbaptized-but-with-explicit-faith catechumens? Do they also condemn the "anonymous Christian" heresy?

I thought that Bishop (?) Webster's orders were doubtful and hence Fr. (?) Dominic Crawford's (since Bp. Webster ordained him, am I correct?). I'm willing to change my mind. Is there any evidence that their orders are valid?

I knew a couple SSPX priests who taught what was simply St. Thomas' teaching that explicit faith was necessary for salvation, but, no they did not "condemn" the implicit faith theory.  They're no longer with the SSPX.

I think Bishop Webster's orders are good.  Bishop Webster was consecrated a Bishop by Bishop Slupski, who in turn was consecrated by Bishop McKenna, who was consecrated by Bishop Guerard des Lauriers, who was consecrated by Archbishop Thuc.  So there's no issue there.  Bishop Webster was ordained to the priesthood by Bishop Henneberry.  Bishop Henneberry was ordained a priest by Bishop Carmona, who had been consecrated by Archbishop Thuc.  Bishop Henneberry was then consecrated by Bishop Terrasson.

So the weakest link would be the link between Bishop Webster's priestly ordination through +Henneberry through +Terrasson.

+Terrasson was consecrated by the famous or infamous Clemente Dominguez, of Palmar de Troya fame.  Now, Clemente was certainly a valid bishop, but the question might be whether Clemente could validly perform a consecration, since it's a bit of a complicated rite, and Clemente had zero seminary training.  But one of the co-consecrators was a Bishop Puga (also consecrated by +Thuc).  +Puga had been trained as a priest before Vatican II, so he could be presumed to know what he's doing and validly consecrate.

So the one remaining question is that +Terrasson was ordained originally by some Old Catholics, and I didn't know if there had been any record of a conditional ordination (since OC orders are doubtful), but someone here on CI posted/presented the certificate of Terrasson's conditional ordination on the day before his consecration.  So that was the last missing link.

So, based on all that, the weakest link would be whether +Dominguez was able to correctly perform the conditional ordination of +Terrasson.  He did also have assistants from pre-V2-ordained priests for the ordination, though those priests would not have been officially co-ordaining him.  But this would appear to be a merely negative doubt, and so validity should be presumed.