Depends. Some enemies depend on backgrounds, some on blocks, and many other factors. In the case of the dungeon and jungle temple, the backgrounds matter so make sure to keep those. If the blocks are necessary you can always get more of those to place down, just make sure not to get rid of background

Do enemies spawn to their respective biome  background wall (ex. Lizards in jungle temple walls) or to their biome tile (ex. Lizards and jungle temple brick) assuming both are naturally generated?

I'm asking because I'm planning on destroying a world for a blank canvas for farms. I don't know if I need to keep the dungeon/temple/desert background walls or keep dungeon/temple/etc. bricks.

TL;DR do biome specific enemies spawn because of tiles or wall

Enemy farming question