And it totally makes sense, because Peridot started working with the Crystal Gems out of self-preservation, to stop the Cluster, and while she is starting to appreciate some of them on an individual level, she really hasn't had her base assumptions challenged thoroughly yet. It also makes sense, while being quite sub-optimal, that the Crystal Gems should react that way to her. And therefore, through solid characterization and good writing, we have: yikes!
(The gun on the mantle: that middle level of the moon base, with the black thing floating in liquid-ish stuff. Also White Diamond in the murals, but I assume that's much further down the road since she didn't even get a verbal mention.)
(For background, literally, on the Great Diamond Authority—love that they're explicitly a matriarchy—see Wikia on gem symbols, many of which references undoubtedly will be brought into the Great Diamond Authority page as time permits.)
(Edit: this does put a mild crimp in the "Rose Quartz was once Rose Diamond" theory, which has been created based on the above symbols, because if all gem types have the same shape gem, which seems likely based on the Rubys, then Diamonds have, well, diamond-shaped gems, per the murals; and so it wouldn't be as simple as renouncing a title, she'd have to actually change her gem, and that seems . . . difficult. She may have been very high up in Rose Diamond's hierarchy, though, and Rose Diamond got kicked out as a result of Rose Quartz's actions.)
(Edit 2: ugh, I can't believe I made screencaps, even though other people will be all over this. When they first enter, you can see the bottoms of two murals (screenshot 1, screenshot 2), which look blue and pink; the blue has an asymmetric bottom, and the one that Peridot says is Blue Diamond is facing sideways, while the pink one has a sea-shell-y bottom. The one Period says is Yellow Diamond has a different bottom, with a protruding central point (her face, just for kicks). So Rose Quartz = Rose Diamond, not confirmed (though it's notable that we do not see Rose Diamond's face alone of the murals), but that there was a Rose Diamond I think is indisputable. Also: White Diamond, I presume?)
How fucked up was that Earth map?
Finally, Lion <3!