This is purely my opinion, and I hope people don't get too angry at me. I realize I'm probably a fundamentalist's worse nightmare...
I was told in 6th grade by my religion teacher that everything in the Bible is True, but not everything is fact. This is something that I definitely believe. Some things may have actually happened, but I can also deal with it if it was merely a story to convey a message, God's message.
The construction actual of the Tower of Babel may or may not have happened, but I don't think it's something to worry about. The point is this: The people were trying to exalt themselves and show their own greatness--maybe even try to become equal to God. They were building not to glorify the Lord, but themselves.
(Genesis 11:4) God did not like their rebellious actions and scattered them.
Moral of the story? Limit your pride. God is God, and we are not. God humbles those who exalt themselves.
Our intentions for exploring space is not to reach heaven. Maybe we are trying to show our own greatness (competition with other countries), but we are not trying to become gods in this way.
Plus, I feel that we now know that if we continue to travel upward, we won't bump into heaven.