Hmm no, the first thing they find out about each other is that they are related.
While it is brought up in the story, the understanding I had is that they didn't believe it, when they have their falling out, the idea they are related is the first thing that gets thrown out of the window, and when Mifuyu confirms it to them at the end, their reaction told me they weren't just being hurtful due to being upset, it was what they truly believed at the time.
Well if anything I think that reinforces their bond being formed through being sisters. When they got along well, they were sisters; when they hated each other, they rejected that bond. The fact-checking from the doctor is a coincidence that furthered them being willing to be open with each other again. I also think they were more taken by the anecdote of them holding hands moments after birth than the confirmation that they were twins, which I'm sure they factually believed already. When they stopped talking to each other and disavowed each other as sisters, it was more like how people can disown a child or cut off contact with a family member. They're "not family" anymore, even if biologically they still are.
When I keep saying their relationship is just weird, this stuff is what I mean. The deepest, most passionate, intimate feelings they have of needing each other are just as intensely equated to them being sisters. The more of a bond they have, the more "sisterly" they are. Even though to most outsiders, it appears that the more of whatever connection they have going on, the less familial it becomes.
one particularly steamy piece of speculation points out that their meeting in the shrine reflects the story of the two lovers
Ah yep I thought of that even before watching Tsukasa's MSS actually. When they showed up in the Eternal Sakura event and something was said about them regularly meeting each other at Mizuna Shrine, I was incredulous. Like what are the writers thinking, making them fit into the story about the reunited lovers with such notable parallels. As a side note, I was already shipping Iroha and Yachiyo some time around chapter 3 because of that shrine story. XD
But talking about failing to represent the characters, Alina is one of the ones that get rid the hardest, if she is half a character without both her MSS and her relevant events, she is about a tenth of a character in the anime, were we are barely given context to how she thinks, just that she is wild.
This is hearsay, as again I have not watched the anime, but doesn't the anime only cover up to chapter 6? And Alina doesn't appear much up to that point even in the game?