Chunk rendering issues in F5 mode (Broken block rendering)

The bug

The game's rendering engine doesn't behave correctly in F5 mode when the player crosses chunk borders.

How to reproduce

1. Make a wall at a chunk border, direction (XYZ) doesn't matter
2. Dig 2 blocks into the wall so that the player can fit in
3. Stand in the hole, face the other chunk and make sure that there's a block above, below and next to the player on both sides
4. Press F5 twice to open the front-view and move out of the hole, blocks which weren't rendered while standing in the hole are now being rendered