While themes do look pretty messed up in the new customize page, it’s usually just the preview! Using the new customize instead of the classic shouldn’t mess your themes up too much. I recently tried it out because my codes weren’t working properly in the classic customize page, and found it to be actually pretty nice! If you can get past the weird navigation and annoying sidebar layout. In fact, the new customize page is what I made this theme in!
So, while this is a bit troubling and incredibly annoying and - sigh - just another thing Tumblr’s decided to take away from us for no reason whatsoever, we can get through this!