To take Discovery as prime timeline canon is to assume that so much that was established previously in the franchise is not canon. So either the shows that came before have elements that are non-canon, or Discovery itself is outside of the canon, inside of its own related but distinct universe. A reboot, a reimagining, and the assorted labels are a conceit to that. Which is fine if that is what they are doing, but not when it is not admitted to.
The differences do pile up. There is a decent tradition of squinting to make something fit in franchise canon, but it has not been this stark before. And the official line each time is "trust us, it'll fit". Even the Animated Series, which conflicts in ways with later established canon, was not as difficult to fit into canon. Somehow, Pike's Enterprise looks like this depiction, but reverts just in time for the second pilot. The uniforms look like this iteration, but revert just in time for the second pilot. The Klingons were explained with the augment virus, but are somehow a starkly different species in this, and then revert, and then change to something else that was established as the way Klingons look. There's holographic projector technology that was just being tested in Deep Space Nine one hundred years later. The stuff that should have been the only stuff to quibble about is the phasers looking the way they do, and the relatively minor minutiae that can fit with squinting it into canon. Those are easy enough to dismiss as an issue. But it is stark thing after stark thing that really cannot be dismissed. So retcon, reboot, reimagining, whatever the label, is a conceit that this is not the same history and universe that was collectively presented previously. Again, fine, but they need to just cop to it. Frankly "this is prime timeline" is just a marketing tool and PR doublethink.