Please provide more context for your question and a better photo. What furniture do you have or plan to have? What rooms are these?

The room behind it is the dining room

I’d keep them, built in shelving is really nice to have, but I’d add a back to it so the dining room side was just flat wall

I would keep them too. Fun project to have backing added on dining side. Remove bottom shelf to open up more to display tall objects, and paint or wallpaper back of shelves to compliment the room decor it’s facing.

No! i like them. adds interst to the room!

It really depends on what you want to use these rooms for. Also, do you want more open rooms or do you need to keep the two room functionally separate?

I need a lot more context and you need to live there for a wahile before making major changes . I do not like shelving to display many things really not worth display and I for sure would not make the shelving with a back on it to form a wall between the 2 spaces without a huge amount of thought .

I would cover the backs too. Definitely I would keep them.