This work presents visual morphological and dynamical classifications for 637 spatially resolved galaxies, most of which are at intermediate redshift ( $z\sim0.3$ ), 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 ( $r\lt20$ mag) high-confidence ( $\gt0.98$ ) morphological classifications at redshifts ( $0.2 \le z \le0.4$ ), 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 $z\sim0$ is established at $z\sim0.3$ . We suggest that galaxies without obvious stellar rotation are dynamically pre-processed sometime before $z\sim0.3$ within lower mass groups before joining denser environments.