There's no such thing as "active perception." I get that it's often offered as a shorthand to describe rolling a Wisdom (Perception) check but it needlessly confuses what a passive check is. Passive checks refer to there being no roll, not that the character is somehow "inactive."
When passive Perception applies, the character is staying alert to danger in an ongoing basis and the result of that effort is uncertain. A character is not alert to danger when he or she is performing an ongoing task like navigating, tracking, foraging, drawing a map or any task that is at least as distracting. So, a character that is doing those tasks is simply surprised, no check. The exception is a ranger in favored terrain who can stay alert to danger while doing other tasks. If you want the players to choose to do something other than have their characters stay alert for danger, the DM must either mandate certain tasks in particular situations (needing to navigate in a trackless wilderness, for example) or offer a significant enough benefit to risk automatic surprise when a lurking monster turns up (e.g. a source map is worth gold back in town).
In combat, most creatures remain alert to danger and so its passive Perception applies when trying to determine if a monster can hide or the character spots a trap or hazard. This effectively makes the passive Perception score a "floor" for the Search action.
Outside of combat, a player must be reasonably specific about where and how a search is conducted to have a chance to notice a hidden object. If the outcome of that search is uncertain and there's a meaningful consequence of failure, the DM may then call for a Wisdom (Perception) check.