A noun that describes a person or group that sees all sides of an argument but doesn't have any opinions on it or make any judgements?

An impartial observer or dispassionate observer.

Impartial

not partial or biased : treating or affecting all equally

MW

or dispassionate.

not influenced by strong feeling
especially : not affected by personal or emotional involvement

MW

I suggest fence-sitter

fence-sitting

a state of indecision or neutrality with respect to conflicting positions

Or you could go with

fly on the wall

having or involving an inconspicuous but effective point of observation fly-on-the-wall observations of aspects of daily life — Will Manley

Or perhaps

armchair

1.remote from direct dealing with problems : theoretical rather than practical armchair strategists

2: sharing vicariously in another's experiences an armchair traveler

[Merriam-Webster]