Droning Bureaucrats's ability affects all creatures with mana value equal to exactly X, regardless of whether they were on the battlefield at the time the ability resolved. For example, if the ability resolves with an X of 4, then Giant Solifuge is put onto the battlefield, the Solifuge can't attack or block that turn.

Creature lands and most token creatures have mana value 0. If a creature on the battlefield has {X} in its mana cost, treat X as 0.

If you use Droning Bureaucrats's ability after you have declared attackers but before your opponent declares blockers, the restriction will apply to only your opponent's creatures. Creatures that are already attacking will be unaffected.