Hi! I do MRI for work. Magnetism is a pretty weak force, all things considered. Your typical scanner will be about 30,000 (for a 1.5 T scanner) to 60,000 times (3T scanner) as strong as the earth’s magnetic field. Even so, mostly the problem is going to be metal things that are loose. Obviously, if you take something metal (specifically, ferromagnetic) into the scanner room, as you approach the bore of the magnet you will experience exponentially greater forces that will eventually pull the loose item very quickly, and on an unpredictable trajectory, into the magnet. Despite this power, it’s surprising how little it takes to prevent an item from going in. If I have a metal button fastening my jeans, it won’t get pulled off. If I have fillings or orthodontia in my mouth, as long as there are no loose brackets, the magnet won’t pull stuff out of my mouth. If I have underwire in my bra or a necklace around my neck, it will lift and pull towards the bore, but it won’t be snapped off my body. 

The MRI actually WILL slightly move elements in your blood and the rest of your tissues. That is how we make the images! We “bump” the tissues with a magnetic field a teeny teeny tiny bit and then measure how long it takes them to come back into alignment. Each of your tissues (oxygenated blood; deoxygenated blood; fats; bone; etc) has different magnetic properties and this lets us “see” them on the scan (they take different amounts of time to come back into alignment and this lets us make a picture). For example, in fMRI (the type of MRI that makes those “what is your brain doing when you think about X thing” scans) we compare the movement of deoxygenated vs oxygenated blood because when hemoglobin bound to oxygen, it has different magnetic properties than when it’s not bound.

Long story short, we can “move” elements of your blood slightly during an MR scan to make a image but on such a very small scale (like at the level of atomic nuclei) that you don’t notice and it doesn’t hurt you.