Interesting experiment, but two groups seems like a too small a sample.
If moderation is done by humans, you could simply prove that one moderator had a worse morning than the other, or that through luck of the draw Group A went to a sympathetic moderator while group B did not. That could demonstrate individual bias, but not institutional.
If moderation is automated, how do you control for the weight of keywords, phrases, etc? Maybe Group A was full of statements that almost threw a flag but not quite, while Group B contained mostly innocuous wording but (only) one phrase that actually got flagged.
If both groups were designed to be unpleasant, but various "blacklist" words and phrases are weighted differently, Group A might have achieved "flagged" weight while group Group B was "flagged -1." One might have scored 99 pts vs 100 for the other, but the visible difference is that one remains visible while the other does not.
Thinking out loud, now... let's say that Facebook does have a political bias. How do you prove that Facebook's financial success is despite that political bias, and not because of it?
Is it possible to have a monopoly on digital socialization? If you can't declare Facebook a monopoly, and therefore subject to greater regulation, then your only lever over Facebook is social pressure, presumably in the form of bad press and boycotts, which will reduce their advertising revenue. How do you prove that the existing political bias is leading them to sub-optimal revenues?