Saying this implies that anyone can get a flair, so long as they are not brigading. This is not true, even according to the moderator comments. "Only mods can assign User Flair, and User Flair is only for conservatives"[0].
So no, going flair-only is explicitly to silence those of differing opinions.
Don't get me wrong, they are well within their rights to do so, it is _their_ subreddit, after all. However, if they're going to dance around and act like a bastion of free speech, maybe it's time for some introspection.
[0] https://www.reddit.com/r/Conservative/wiki/index/flair_rules...