We are taught not to question the shape of the Earth as surely as we are taught not to question that 2+2=4....
Were we all? If so, upon what evidence do you make this claim? If I told you the story of an eight-year-old in grade school who questioned why 1+1=2, and was subsequently shown the proof by a teacher who understood the importance of questioning things, would you believe me, or would you dismiss my story as mere fantasy? Granted, that young boy didn't understand the proof at the time, but he did search for it...
To respond to the OP: NASA has pictures and eyewitness accounts of a RE; FE theory has claims of conspiracy without evidence. In this respect, the RE approach is scientific, and the FE approach is not (at least, if I understand it correctly, it is not - correct me if I am wrong, FE'ers). One of the most important parts of scientific hypotheses and tests is falsifiability; those things which are not falsifiable cannot be approached in such a manner. While NASA pictures and eyewitness accounts are falsifiable, conspiracy theories (along with the "invisible sky fairy [that] is judging everything we do") are more or less not falsifiable. In addition, RET is complete enough that the pictures and accounts from NASA and the other space agencies are not at all far-fetched.
That being said, FET presents an intriguing case for a FE. It's not a complete case, though (see, for starters, my thread asking about the stars in the southern hemisphere).
FE theorists often use their perception of the earth up close as a good reason to postulate that the earth is flat, not realizing that by accepting what they have been taught about planes and refusing to question the perceptions that arise from what they have been taught, they are doing exactly what they (perhaps rightfully) claim REers are doing.
So, to summarize, I believe the earth is round because the evidence that I have seen points to it. As to things unexplained, I choose to believe in the existence of the gravitron (yes, one of the hypothetical aspects of physics) rather than an ever-accelerating earth because it is a better fit for what I have observed, what other people have observed, and the workings of the earth in general. Am I taking a leap of faith in believing the physical laws taught to me? Yes, but coupled with the fact that those laws are generally observable and always consistent, that leap of faith isn't so far fetched. To me, it's a little bit like walking out one's door in the morning and thinking, "The planet beneath my feet appears to fit what I have been taught and observed about flatness, and therefore, I will believe it is flat until proven otherwise."
Hope that makes sense; it's kind of late here, so my mind is not working properly, and this probably ended up being a long rant (I'll edit it tomorrow, maybe). Also, please note that I would not read a thing on this site if I were not interested in questioning those things I have been taught and observed.