There are no metals
in the mRNA vaccines and that includes the mercury based additive Thiomersal which is what the conventional anti-vaxxers generally object to.
But additives are what accounts for the small but consistent number of immediate allergic reactions.
The human body is very mildly magnetic, owing to a fairly high concentration of iron. But not to a degree that it would exert any discernable force on an object of hardly any mass at all.
BTW, worth recalling that QAnon first made significant penetration among anti-vaxxers- presumably both the crunchy variety and the homeschool Mom types. I think anti-vaxxers are primarily people who are unwilling or incapable of accurately assessing data so they trust whomever pushes their buttons.