This is a very oddly phrased question, given that the position of the church is that homosexuality is disordered, but gay people are not inherently living in a state of sin. I recommend that the title and description be updated to match the resolution criteria.

most of the top candidates have known opinions on this:

Pietro Parolin: 28% (YES)

Luis Antonio Tagle: 23% (NO)

Matteo Zuppi: 10% (NO, a bit uncertain here but more likely no)

Pierbattista Pizzaballa: 9% (YES)

Péter Erdő: 6% (YES)

Peter Turkson: 5% (YES)

Fridolin Ambongo Besungu: 3% (YES)

Robert Sarah: 2% (YES)

Anders Arborelius: 1.1% (YES)

José Tolentino Calaça de Mendonça: 1% (NO)

Fair value based on this: .57 as of current standings in the pope market. At the very least Tagle is most likely a NO so this should trade below 1 - p(luis antonio tagle). I bought it down half the way: i'll let someone else do the rest.

How does this resolve in a case like “being gay is not inherently a sin but acting on it is” or the like?

@GleamingRhino great question that I should have thought of earlier. I think it's fair to resolve yes in that situation. The title for this question was originally going to be "will the next pope be anti-gay?" And that's still essentially what I'm trying to ask. I changed it in an attempt to be less subjective.