As Kad said, the Public is not the primary producer of Fun Home, so technically it isn't two siblings fighting to be the favorite son. Fans are putting them in that position because they're two well reviewed and well received shows that began in the same place.
Or it could be that some fans want to spread the, "Yay! Great new works from the Public!" high just a little longer. If you could get a quality new show (as deemed by reviews and responses) two years in a row, you want to go for that.
Correct me if I'm wrong, but May 3 doesn't *have* to be closing date, correct? I thought they could do another brief extension before another show moves in?
From the Public's POV, they'd like bragging rights for two back-to-back hit transfers in back-to-back seasons. Although not a lead producer on FH, they'll make a few bucks on it, and it could win Tony's, so why throw AH in its way?
^^^ That too. While they're already a very well respected name, more never hurts. Whether that's a true reason or not, I don't know. But it fits in with the share the wealth notion.
A transfer seems inevitable. The date is the question now.