Ok so if you have 20 dexterity, expertise in stealth and a proficiency bonus of 6 you can achieve a score of 37. On a crit fail. You have a maximum of 57. If your DM does RAW rules, ability checks don’t have crits, only attack roles and saving throws do. This is essentially an insta-vanish taking 1 minute+ 1 action.

How to do it: 

10 ranger

1 rouge/bard OR skill master (TCoE) feat. Do stealth.

Pass without trace

With ranger’s 10th level feature you gain a + 10 to stealth and with PWT you get a +10. Prof of 6. There you go, steal whatever you want, no one will ever notice. To maximize an ionstone that grants prof. +1 and 5 tomes of quickness of action (or 500 years, your choice) you can get to a minimum of 43. Maximum 63.

i mean.. if you're level 20, laying perfectly still in the mud, and you have pass w/o trace up, and you're an expert and you have maxed stats. In that very specific circumstance your stealth is very high. but it also required asi investment (maxing dex) a spell, a class feature that is just.. almost always inferior to it's tasha's variant, and expertise.  In that situation you SHOULD be unreasonably good at the thing. You put in the work, that's the payoff. It's also not ~passive~. As soon as you move you loose 10 points of that bonus. and you still need to follow all the rules of hiding. (breaking line of sight, moving quietly, not attacking). 

I don't see any of this as "OP"

Alternative:

(1) Be a 2nd level Druid.

(2) Wildshape into a normal spider.

(3) Go wherever you want because no one thinks twice about a spider.

Spiders?  I am scared of spiders!  Wildshape lets you be Tiny, as there is no smaller size category, and that's about as big as your fist!  I'm absolutely going to react poorly to seeing a spider that big!  Then again, Druids are pretty sneaky.  They can use Pass Without Trace at 3rd level before turning into a great big spider.  I'd probably never notice unless I got bitten.

"Tiny" only refers to the space "occupied" by the creature, not the creature's actual size and weight. Anything smaller than Small is defaulted to Tiny. A strict DM might restrict a Druid to creatures with published stablocks for simplicity, which would indeed imply a fairly sizable spider, but it's pretty reasonable to assume that the world of D&D includes a normal ecosystem. Anything too small to be an individual threat is usually just treated as narrative flavor, or an environmental hazard.

Though, Wildshaping into diminutive creatures obvious comes with mechanical benefits like this, so it's also reasonable to apply further restrictions, as they do for swim and fly speeds.

Wildshaping into a spider may not always be best given that many are afraid of them but there are other forms that are usually more innocuous.

Cats, birds, rats, dogs, squirrels

For sneakies, I do recommend a Rogue - Shadow Monk. Pass without trace, shadowporting, silence, and stealth expertise. Throw in some Shadow-Touched feat for a free Invisibility and Disguise Self? Even better if you're a tortle.

Any larger creature would look pretty out of place within someone's home or shop. Squirrels, no matter how cute, are up to something.

However, in the typical medieval fantasy setting, a layer of grime over everything is pretty well taken for granted. Most doors won't quite seal shut, and a lack of central A/C or refrigeration means that windows are going to be left open and food is going to rot, which ultimately means that spiders are going to be so common that anyone with a meaningful fear of spiders is living in the wrong timeline. Modern/western sterility/hygiene is pretty extreme compared to even just a few decades ago.

Due to calcs done, you have a theoretical max of 187. On a max damage crit with 5th level divine smite (18 ranger, 2 paladin) and dhampir (UA) and a stealth crit above with post 1 mentions.

Quote from Memnosyne >>

Alternative:

(1) Be a 2nd level Druid.

(2) Wildshape into a normal spider.

(3) Go wherever you want because no one thinks twice about a spider.

 Yes but can you grab and carry loot?

Quote from Memnosyne >>

Any larger creature would look pretty out of place within someone's home or shop. Squirrels, no matter how cute, are up to something.

However, in the typical medieval fantasy setting, a layer of grime over everything is pretty well taken for granted. Most doors won't quite seal shut, and a lack of central A/C or refrigeration means that windows are going to be left open and food is going to rot, which ultimately means that spiders are going to be so common that anyone with a meaningful fear of spiders is living in the wrong timeline. Modern/western sterility/hygiene is pretty extreme compared to even just a few decades ago.

 
pity then, that you couldn’t wildshape into a slime.

 (edited for bad typing)

Quote from Bluepanther512 >>

Quote from Memnosyne >>

Alternative:

(1) Be a 2nd level Druid.

(2) Wildshape into a normal spider.

(3) Go wherever you want because no one thinks twice about a spider.

 Yes but can you grab and carry loot?

Sure, either revert back to a human form to fill a bag before wildshaping to escape, or just grab whatever it is, and wildshape directly into a different spider to absorb it into your form, strength permitting.

A high stealth check result doesn’t make you invisible. You still need to be hiding in/behind something. You can’t just roll, walk into a store, and start grabbing things. It’s not Skyrim, you can’t just crouch in front of someone and run their pockets. 

Now, this does mean you’re moving so quietly as to be effectively silent, and as long as you do have a place to hide no one will see you. 

But you still need to pick that lock to get into the vault. You still need to roll Sleight of Hand to pocket that item discretely and quietly. 

Stealth doesn’t break those things. You can’t just walk around and take anything you want because of a high Stealth check. That’s not how it works.