Mais ils ont voulu me faire filer avant que je le vois / voie.
Or does "avant que" always have to be followed by the Subjonctif, even in casual speech?
Avant que always needs the subjunctive.
The subjunctive has nothing to do with formality. The best example of this is hearing a teenager announce to his friends il faut que je m'en aille.
Although the ne explétif isn't obligatory according to some, I would use it in your sentence.
It's syntactic role is to emphasize semi-negation. Action not being held/never going to be held.
Full sentence would be :
[...] avant que je ne le voie.