This work presents visual morphological and dynamical classifications for 637 spatially resolved galaxies, most of which are at intermediate redshift (z ∼ 0.3), in the Middle-Ages Galaxy Properties with Integral field spectroscopy (MAGPI) Survey. For each galaxy, we obtain a minimum of 11 independent visual classifications by knowledgeable classifiers. We use an extension of the standard Dawid-Skene Bayesian model introducing classifier-specific confidence parameters and galaxy-specific difficulty parameters to quantify classifier confidence and infer reliable statistical confidence estimates. Selecting sub-samples of 86 bright (r < 20 mag) high-confidence (> 0.98) morphological classifications at redshifts (0.2 ≤ z ≤ 0.4), we confirm the full range of morphological types is represented in MAGPI as intended in the survey design. Similarly, with a sub-sample of 82 bright high-confidence stellar kinematic classifications, we find that the rotating and non-rotating galaxies seen at low redshift are already in place at intermediate redshifts. We do not find evidence that the kinematic morphology-density relation seen at z ∼ 0 is established at z ∼ 0.3. We suggest that galaxies without obvious stellar rotation are dynamically pre-processed sometime before z ∼ 0.3 within lower mass groups before joining denser environments.