You should be just fine with an airline career - your distaste for negative or zero G maneuvers will be echoed by your fare-paying passengers in the back. Any positive G's will ,as stated by Cessna I Plate, be limited to steep bank turns - rarely above 1.5.
I should think that during training , the only below 1 G procedures might be an emergency descent - where if you can do it a nose down combined with a high bank angle should limit your exposure to that......correct me if I am wrong...........
So unless you are a cowboy 707 test pilot, aerobatics and the G forces that come with them are not a requirement for the job.
cheers,
vapilot