Couldn't find official articles, just more forums. At least for Catholicism.
Update: Aha! I found out that Judaism SE actually has a post for this. What is the halachic status of adult conjoined twins? Your move, Christianity SE! XD
Abigail Loraine Hensel and Brittany Lee Hensel (born March 7, 1990) are American conjoined twins. They key thing here is that they (are female and) have '1 set of reproductive organs' unlike Hannah Kersey or Hazel Jones.
So what does Catholicism say about marriage for conjoined twins like them who share reproductive organs: Can they indeed get married (to separate males)?
In particular, are they indeed allowed to have sex with their respective spouses even if obtaining carnal knowledge of 1 twin is equivalent to obtaining carnal knowledge of the other? Like... If Abby marries Carl and Brittany marries Daniel, then can Carl / Daniel have sex with Abby / Brittany even if it means Carl / Daniel would be obtaining carnal knowledge of Brittany / Abby?
Consider the following scenarios that may arise:
If Carl and Abby are allowed to have sex and they do have sex, then after they are done, can Brittany and Daniel begin right afterwards? Can all 4 do it at the same time like alternately? Or does it have to be 1 pair after the other?
If Brittany isn't seeing anyone, then is it wrong for Brittany to ask Abby to have sex with Carl on a day Abby and Carl weren't particularly intending to have sex (but then Abby and Carl of course consent anyway) because Brittany wants sexual pleasure kinda like how Jews would ask non-Jews to operate electrical switches?
Edit: There's a deleted comment that said I was lecherous or something unless I was actually 1 of the conjoined twins or 1 of the prospective partners. The comment made it seem like I have a fantasy of having sex with conjoined twins. Lol. I counter-argued that I'm no different from asking 'Can Henry VIII marry his brother's widow?' I suppose everyone from 0 AD to 1400 was lecherous if they asked if people could marry their sibling's widow? (Afaik the case with Henry VIII is that apparently people couldn't marry their sibling's widow under Catholic canon law at the time, but then there was a papal dispensation granted for Henry VIII. But then sometime later Catholic canon law changed so that people could just marry their sibling's widows.) And if I were 1 of the prospective partners, then how would I prove it? Do you want me to submit an ID and an affidavit to the moderators? LOL.
10 hours ago I submitted this comment flag quoting Terry Tao:
So one should be unafraid to ask “stupid” questions, challenging conventional wisdom on a subject; the answers to these questions will occasionally lead to a surprising conclusion, but more often will simply tell you why the conventional wisdom is there in the first place, which is well worth knowing.
But it was declined. LOL.