My understanding is that general relativity concludes that gravity isn't real because it does not exist in all frames of reference. Also that mass and energy warp spacetime into a curved geometry. Does that then mean that objects in orbit are actually traveling in straight lines in curved spacetime?
Your first line is incorrect, gravity is real, just jump up and you will confirm that. Frames of reference are used to find how gravity affects our measurements of spacetime.
Your second line is correct.
Objects, from photons to planets, moving in general relativity, obey the geodesic equation, so a curved line can be a "straight line", that is, if you define a straight line as the shortest distance between two points.