Did the pre-Norman Saxons buy into the idea that their own vernacular was more barbarous that the Church's preferred language?
This was a vernacular Germanic alliterative verse narrative. To translate it into Latin would not only serve no purpose from the point of view of the Church. It would be decidedly difficult (as the alliterative verse formula would need to be abandoned completely). Moreover, not everyone in the church was keen on the idea of promoting the creation of such texts, and Beowulf might indeed have raised some eyebrows, in its time. But this would have nothing to do with the language of its recitation, and everything to do with its content.
The Northumbrian scholar Alcuin (735CE – 804CE) was a noted opponent of the practice of reciting and maintaining originally pagan or secular verse, and is attributed such pointed gems as, for example,
"Quid Hinieldus cum Christo?" ("What has [the legendary warrior] Ingeld to do with Christ?")
"Nec audiendi qui solent dicere, Vox populi, vox Dei, quum tumultuositas vulgi semper insaniae proxima sit." ('And do not listen to those who keep saying, 'The voice of the people is the voice of God.' because the tumult of the crowd is always close to madness.')
While Latin was the principal scribal language of the English Church during the Early Middle Ages, the work of translation to the vernacular (not just of the biblical text, but of Hagiographies and didactic texts) went on apace. The notion that Anglicanism saved the Church from a former longstanding slavery to the Latin language is a notion which emerges later, but there is no period to which it can be accurately applied.
In short, texts like that of Beowulf are certainly recorded as having their opponents, in the English clergy. The language of Beowulf is not, however, the issue here. Rather, its at best secular and at worst pagan nature is.