Every time this comes up I basically write the same response... I wish DSC was in its own timeline, separate from the Prime and Kelvin timelines.
I'm fine with them taking visual and narrative liberties as long as it results in good television, but I know I'm in the minority. Giving DSC its own timeline would basically give it the freedom to do whatever they wanted without worrying about fan outrage every time something looks different than 'The Cage' or 'TOS', much like what the Kelvin timeline films have. But there is a need to keep it separate from the Kelvin timeline, so that's why I suggest a third timeline.
How'd you get to a third timeline? I don't know. I'm not a writer. Ask Worf, he might have a few ideas. Hey, maybe they could find one of those quantum mirrors that Daniel Jackson found?