Why isn't the active color allowed to be in check in a FEN legal position? The title says it. Reading up on how to describe the position of a board, all of the requirements make sense (like two kings not being on adjacent squares and so on) except for the active color being in check. Why isn't that allowed? What is the rationale behind this?
The active color (i.e. the color which has the next move) is allowed to be in check, and as ajax points out, at most twice.

But perhaps you meant the inactive color not being allowed to be in check.  Why is that?  The answer is: if the inactive color is in check, it would mean that at least the last move by the inactive color was illegal, allowing its own King to remain in or be exposed to check.