In Gibbon's great "Decline and Fall of the Roman Empire", he makes the argument that Christianity was one of the main factors that lead to the collapse of the empire. To what extent is this the case? What do other historians think?

Gibbon here is "continuing" the argument set forward by the Late Antique historian, Zosimus who wrote Historia Nova. Also known to some as Zosimus Historicus (the historian), he was alive during the 490s – 510s but no definitive knowledge of his birth date or death date can be procured. Zosimus is interesting because he was a polytheist (a pagan/non-christian) writing in the fifth/sixth century, one of the very few from this time whose works still reach us today. He largely contends that the conversion of Constantine to Christianity had a negative knock-on effect on the empire, implying it to be one of the direct causes for the fall of Rome at the hands of Alaric, 410. For his attitude, see Zosimus Hist. Nov. 51, 115, 129, 150, 159-160; but note he is not uniformly negative of Christianity, just of those who hide behind it to excuse their vices (such as Olympius and Constantine). He did not, as sometimes touted, declare that the west fell in 476. If anything, he saw the fall of the west in 410 (sadly, we do not know exactly why because the later parts of his work are no longer extent).

Now, Zosimus did not intend, I think, to initiate a polemical dialogue which lasted the better part of… two thousand years. By implying that Christianity and Constantine brought about the fall of Rome, Marcellinus Comes, and others for sure, felt as though a counter-argument needed to be made (Croke 1983, 81-119). In 527, Marcellinus Comes composed his first edition of Chronicle (Treadgold 2007, 230; in 534 he extended it to the year 534) which, he claimed, was a continuation of Jerome’s continuation of Eusebius (oof). But what Marcellinus Comes did, and this is where your jaw will drop, he changed the start date of his history to 378/9 (just after the death of emperor Valens, hint hint) and ended it 518. By shifting the start of his history to 378/9, Marcellinus Comes chooses a new boogey man to set the blame for a decaying empire onto: the Goths (Bjornlie 2013, 90-93). This decision was entirely conscious and tactical. He further states (and this is the first time it is mentioned) that the western empire fell in 476 after the ultimate deposition of Romulus Augustulus by the ‘Gothic king’ Odoacer (Marcellinus Comes, Chron., 476.2, 489; Croke 1983, 81-119; Treadgold 2007, 232). Yes, the fabrication of the fall of the west was a Late Antique invention, fabricated 51 years after the fact only as a response to Zosimus’ implication that Christianity brought about the decline of the empire. It is also conspicuous that Odoacer should be called a 'Goth,' given that there is no other evidence to indicate that he was (though this may just be more of that pesky blurring of identities in Late Antiquity: see Meier 2017).

Now we return to your question: to what extent is this the case? To be frank, it may or may not be the case: the answer is factually unknowable. Gibbon followed Zosimus because it was convenient for his world view (see also Croke 1983). Gibbon merely followed what he thought was Zosimus’ angle but also included Marcellinus Comes’. The strict fact of the matter is the entire ‘Fall of the West’ was fabricated by Marcellinus Comes as a propagandistic backlash 1) against Zosimus, discussed above, and 2) as propaganda against the Ostrogothic kingdom especially after his edits in 534. In this time, Constantinople was on high alert to go to war, which it did in the follow year, with Ostrogothic Italy and the work may have been used to influence opinions on the matter. Did the west really fall? This is one of the reasons why many historians now are turning toward the transformation hypothesis instead of the collapse hypothesis.

Hope this helps.

Edits 1&2: dicey spelling