An MRI below about 5-6 teslas is perfectly safe provided there is no ferrous shrapnel in your body. If there is shrapnel in your body, the magnet will pull it out and cut your body in the process.
(The X-ray is done to make sure you don't have any shrapnel and also because it is cheaper. If the X-ray reveals the problem, you can avoid the more expensive MRI.)
RF radiation will only harm the human body at very high field strengths (think microwave oven). The typical medical machine only gets 1-3 teslas, though a few research machines can reach the 6-8 tesla neighborhood (e.g., Dan Sodickson has an 8 tesla machine here at NYU).
I want to be clear: you're saying it's totally safe to get an MRI or a full body scan or whatever else as a totally elective procedure?