What a STUPID poll.
That's like saying, "what would you do if you had to be a Coke or Pepsi fan, and one of them meant going to Hell -- but you didn't know which one!"
God isn't arbitrary, and He is not a tyrant. That is blasphemy!
Only MORTAL SIN can send a person to hell, and it has to, because it completely kills charity/Sanctifying Grace in the soul, drives out the Holy Ghost, and thereby chooses against God. It is a horrible thing.
But it's also real and fundamental.
It's like some foolish people saying, "What if there was a day when all mortal sins were permitted. Which would you commit?" That's a horrible question! We should hate sin because it's fundamentally offensive to God.
God isn't offended by sin "just because" or as some kind of test. It's fundamentally against Him. Why do you suppose there is no sin in God -- and there can't be? Having anti-God traits (a.k.a. Imperfections) is one thing God can't do. He can't contradict Himself, because that is not a perfection.
That's like asking my kids, "If you knew Daddy was in a super good mood, and you KNEW you'd get away with it, which rules would you break and/or which things would you do that normally make him angry?" A good child would answer: "Nothing! None of them!" if they truly loved their dad and wanted to please him.
Anyhow, let's review what it takes to be a mortal sin. So you can receive First Communion next week! (just kidding, but seriously this is stuff we all learn when we're 7 years old). A sin has to
A) Be a mortal/serious sin -- grave matter
B) We have to know that it is a sin
C) We have to fully consent to it.
Flat Earth vs. Globe Earth fails horribly on point B), since none of us can fly up to the troposphere, etc. None of us have personally been to space, much less traveled thousands of miles into outer space. Few of us understand advanced mathematics and physics, to understand intuitively the motions of the stars and heavenly bodies.
I also believe it falls short on point A). Considering it's NOT right in front of our face, we are simply dumb humans who live their lives in a very small sliver of the earth. I wouldn't expect a field mouse on my land to have a full grasp and understanding of the layout of the state of Texas either! So why would God expect us to "figure out" the fundamental nature of the earth and universe? That is a pretty good and fair comparison, too.
Long story short, it's easy to conceive of a person in the state of grace -- a Saint, if you will -- getting it "wrong" on the fundamental nature of the earth and universe. It's one of those things most people can't figure out for themselves with certainty. Knowing that men & women should be together in marriage, ɧoɱosɛҳųαƖity is wrong, stealing is wrong, murder is wrong -- those things are common sense, known in the hearts of all men.
But most important of all, God doesn't play "the shell game" or a game-show with us. We don't have 2 closed doors, A & B, and one of them leading to heaven, and the other leading to hell. That goes for Flat Earth vs. Globe Earth as well as the Pope question. If it's something we can't know with certainty with our puny minds and incomplete information, then God, being perfect Goodness, could not require of us to pass such a "test". It's simple.