Q:

How do I deal with extremely high passive perception?

I recently noticed how crazy high your passive perception can get.
Assuming you are a druid or cleric (i.e. Wisdom being your main stat) with one level in rogue, you can get expertise in perception (2*6 prof bonus). At level 20, with +5 WIS modifier, and with the Observant feat (another +5), that equals to
10 + 5 (WIS) + 12 (prof) + 5 (Observant) = 32 passive perception (+17 to checks)
As a DM, I can hardly make every perception check a DC35 (and shouldn't, since the player would have to invest quite the amount of resources to get such a high passive perception, which should be rewarded).
However, I still might want to add some traps or sneaking enemies without them being immediately spotted. How could I do this, aside from separating the master of perception from the rest of the group every time?

A:

Don't nerf the player's resources
As you rightly say, to get this good has taken a significant investment and it would be a vindictive DM who would invalidate that investment. Feel free to be as vindictive if you like - no moral judgement from me.
Perceiving is not the same as Overcoming
For all sorts of reasons but just limiting to the circumstances you describe:

Traps: DM: "You see a long corridor, the walls have a bas relief with hideous demons, their mouths are dark holes. Super Eyes notices old blood on the floor and that the entire floor of the corridor is disconnected from the wall and the floor you are standing on". The super perception has shown them the spear trap and the trigger - they still have to get down the corridor or go home: perception doesn't help here. Finding out how the trap works is an Intelligence (investigation) check, disarming it is a Dexterity (Thieves Tools) check.
Ambushes: So Super Eyes is rarely surprised (if they took the Alert feat this would be never surprised): that doesn't help anyone else. The rest of his companions have not noticed a threat so are surprised until the end of their first turn of the combat. 

A:

By level 20, PCs should be pretty amazing, but so should their enemies.  A character who has spec'd heavily into noticing everything should under normal circumstances.  However traps could have static illusions/invisibility placed over them, so passive Perception would be less useful, but Detect Magic/True Sight would be more useful.
You could also use multiple hidden opponents - the PC can see all 8 of the hidden archers around the room, but as soon as they tell their party members they loose their shots.
There could be decoys - they spot and attack the first hidden enemy, allowing the second to pass by behind them.
Casters could use darkness and silence to make things harder, or go the opposite way and blind or deafen using bright lights and loud noises.  (There must be an alchemical or spell version of a flashbang somewhere!)
Although these seem to be trying to negate the power that a PC has built their character towards, it could make sense as they would be famous for their amazing abilities, especially at level cap.  If opposing the same enemies they were at level 5-10, then being able to ride roughshod over their traps is reasonable.  When opposing enemies who are the most powerful beings/organisations in existence, then they should know that any single tactic is liable to be foiled.

A:

The short answer is "don't"
If you just so happen to have a very perceptive PC in the party then let them be that. There is literally nothing wrong with it, you could run the game as normal and have no problems. The fact that 1 or even a number of the party could have high perception is a good thing as far as the PC's are concerned, they will probably be happy having someone who can keep an eye out for trouble. 
That being the case consider some more convoluted traps. For example have some traps that don't do anything on their own but arm other traps in a dungeon. Even have some "unavoidable" traps such as a long corridor with a 20 foot long pressure plate on it. 
It may seem unavoidable but actually if 2 people stand on just the first 2 tiles for 6 full seconds, a secret door opens up, offering an alternate route. Just because you see it, doesn't mean you understand everything it does/how it works.
These are extreme cases, I'd suggest only putting them in very specific areas/dungeons that are designed to be a significant challenge. It's a great idea to offer specific challenges to a PC which will be hard but will line up with their skill set as well as give them problems to solve that push the boundaries of their abilities.

