Devon,
Every airline has the exact same policy on carryons:
Every single line employee that you meet along the way has the right to reject your bag.
Every one.
And the airline/TSA will back them to the fullest.
If a TSA agent decides that your instrument should not go through security, IT WILL NOT. Go read the TSA guidelines: every line employee has absolute authority, and will be backed by management.
If the gate attendant decides that your instrument will not go on the flight, IT WILL NOT GO. Same policy applies. I have seen people kicked from flights for asking an impertinent question. No kidding.
If the flight attendant decides that the instrument will not go in the overhead bin/must be checked, IT WILL, or you will get off the flight (and if you raise too much of a fuss you can be arrested).
So, the questions you should ask (rather than some specific airline):
Will someone be in a bad mood, and take it out on me?
Will the flight be oversold?
Do the people in question hate guitar players, because they just broke up with one?
These are the sorts of fickle things that could destroy your instrument.
Just in case it isn't already abundantly clear: an airline can have any policy they want, but if the flight attendant/gate attendant decides otherwise, that will be the official airline policy with regards to you and your flight.
Finally, I want to separate reality (the above) from my opinion, which is that this is really, really messed up, and makes me feel like I'm in a police state.
Bradley