Both your and the other counterexample are talking about something other than nonpartisan ballotting, though. I mean, yes, if you have a third party candidate in isolation then whoever that third party is going to "steal" more votes from is going to oppose it.

So democrats would oppose a Green or other progressive candidate in (most races in) New York, sure. That's just self-interest. But for the same reason they'd clearly welcome a libertarian entrant. That's not responsive to the discussion.

The claim upthread was that "both" parties oppose ranked choice voting. And that's simply not true.