Based on the orals there are 4 votes against Idaho (3 liberals + ACB), and 3 against (Thomas, Alito, Gorsuch), so we're down to Roberts and Kavanaugh. My guess is they hold Idaho's law violates EMTALA in a lot of instances and not all of them.
even if that's a correct description of ACB's mien and relative position among her colleagues, she's notably to O'Connor's right (O'Connor joined the per curiam majority in Planned Parenthood v. Casey; crafted the affirmative action consensus this SCOTUS has gutted; opposed public school prayer)
She also joined a bunch of campaign finance restriction majorities whose work completely unraveled under Roberts
Re the Establishment Clause, O'Connor wrote this in 2005! She insinuates 10 Commandments in courtrooms = al Qaeda!
scholar.google.com/scholar_case...
it's difficult to say when the petitions and grants are moving so far to the right. she's joined the far-right cons on the racial gerrymandering cases
I haven't followed where she's been swing-y on casting votes. I know she's joined the three liberals on a few death penalty matters