As one of the prime contributors to the interstellar medium energy budget, magnetic fields naturally play a part in shaping the evolution of galaxies. Galactic magnetic fields can originate from strong primordial magnetic fields provided these latter remain below current observational upper limits. To understand how such magnetic fields would affect the global morphological and dynamical properties of galaxies, we use a suite of high-resolution constrained transport magnetohydrodynamic cosmological zoom simulations where we vary the initial magnetic field strength and configuration along with the prescription for stellar feedback. We find that strong primordial magnetic fields delay the onset of star formation and drain the rotational support of the galaxy, diminishing the radial size of the galactic disc and driving a higher amount of gas towards the centre. This is also reflected in mock UVJ observations by an increase in the light profile concentration of the galaxy. We explore the possible mechanisms behind such a reduction in angular momentum, focusing on magnetic braking. Finally, noticing that the effects of primordial magnetic fields are amplified in the presence of stellar feedback, we briefly discuss whether the changes we measure would also be expected for galactic magnetic fields of non-primordial origin.