I think the reason some people might believe this claim is because we’re taught in school that the moon’s gravity causes the tides. I think the reasoning goes, “well if the moon’s gravity can affect the tides, surely it can affect smaller things too”
It’s a very small force. If you consider such small forces to have an effect, you must also consider gravitational pull of objects that have the same or a larger effect: passing trucks, entering buildings, passing a mountain, going upstairs, going underground.
Also, all movement will cause same type of force on you (acceleration) plus change your body’s alignment to Earth gravity has a large effect on gravity’s pull on organs: shifting position, leaning, walking, driving, taking an elevator, lying down, figeting, trying to stand on a wooden floor, all have several orders of magnitude more effect on you than the moon.
In short: You can’t hear someone whispering ten rows behind you at a Metallica concert.