Skip to the end if you just want examples.
Whether it's due to people projecting their insecurities onto a type, or using the type as an excuse for dysfunctional behavior, INTP gets an appallingly inaccurate and bad image about what truly encompasses the type, and it really is not helpful towards anybody for the community to keep accepting these stereotypes as truth. MBTI is supposed to be a helpful tool to gain an understanding of how someone's brain might work, not a tool for 14 year olds worldwide to use as a get out of jail free card to cleaning their rooms and learning what empathy is.
You know who you are.
I'm not going to go through every single stereotype, but I am going to state that you not knowing what soap is, being an emotionally stunted manchild, and having a penchant for never leaving your house are NOT intrinsic to INTP. They're intrinsic to you needing psychiatric intervention, but not to INTP.
By the way, I think many folks need this reminder: Emotions are not irrational. Emotions are actually just information about yourself. Underlying beliefs produce emotions. Have an emotional response to something? That's an underlying belief. Even right down to preferences for food and appearance.
"But ArminsMother, so many INTPs act like that!"
Yes, most certainly they do. But again, these are not inherent characteristics. While how a type acts when unhealthy is a factor in determining which type you are, it is largely small; coping mechanisms and unhealthy habits tend to be unique to each individual and are heavily influenced by your life experiences, trauma, attachment style, mental disorders, etc.
When I was young (under 25 or so), I did indeed embody many of the stereotypes, but also subverted them. I was emotionally detached from myself and often numb, but also had explosive anger and extreme crying fits, and often felt miserable. I had not been given a good manual to life nor the support I needed to have even a mediocre life, so the end result was a severely emotionally dysregulated, depressed, terrified INTP teenager who desperately wanted someone to save her from her hell so she could finally feel at peace again like she did as a young child in the woods. When a person undergoes trauma, particularly severe trauma, they're likely to develop other functions outside of their stack to cope and/or grow. Eventually, this was Fi for me, but it took a long time.
What does a healthy INTP look like?
Technically speaking, the only thing you need to be an INTP is to relate to the four functions assigned to your type. In other words, if the way your brain processes information is accurate to the functions, you are most likely indeed that type. The functions don't actually speak a whole lot to your ability to be kind, empathetic, have strong morals, feel a lot, any of that. They only speak to how your brain processes, stores, labels, and prioritizes information.
Honestly, that's probably how I got here. The INTP's cognitive stack is a near perfect mirror to how my mind operates on normal settings. Of course, everyone is able to use any function out there and develop it well, too. This is a part of growing up and becoming mature and healthy. As I said above, I had to develop my Fi to learn how to be selfish, live for myself more, and understand my emotions and why I was feeling the way I did. I use it together often nowadays with Ti and Ne to help me navigate through life.
In general, a healthy, well-rounded person of ANY type should be able to:
Name, validate, and process their emotions; be self-aware
Develop rational and reasonable morals based on factual data, logical reasoning, and the complex reality of the human condition
Take adequate care of their basic needs; bathe regularly, eat decently well, move their bodies on the regular
Show compassion, curiosity, and kindness to themselves, others, and perhaps the world
Be accountable and responsible with their behaviors, money, relations, substances, etc.
Not a single one of these precludes you from being an INTP. Every person of every type is capable of achieving all of these with proper support systems and insight into what goes on in their mind.
Examples Of Healthy INTPs
The best example I can think of of a healthy INTP is HealthyGamerGG, who is a psychiatrist that uses his expansive knowledge and well-developed Fe (and Fi; remember, anyone can develop a function not in their stack) to help other people gain broader knowledge about the landscape of society and their own minds. Another fabulous but fictional example is Pieck Finger and Armin Arlert* from Attack On Titan. They are two characters on the opposite sides of a conflict who use their rationale, intense perceptiveness, and broader ability to deduce and conclude things to further their personal goals, as well as the goals of their side in the conflict. Pieck is what I would consider the stereotypical healthy INTP; she is a woman who has a keen eye for small details, an excellent memory, and a calmness to her that only sometimes fails her. She also is motherly, compassionate, has a strong care for her friends and family, and is not afraid to scream in fear when faced with running down a steep piece of bone several thousand feet in the air.
Armin, on the other hand, is an equally if not even more logical and perceptive individual who carries the show through each of its twists and turns, riding on his deductive skills and careful planning to save dozens, and eventually millions, of people. His logical mind is at the forefront most scenes he's in and the driving force behind his character. In fact, the very first scene we ever see him in is him getting his ass beat for having heretical beliefs and theories about the outside world. However, despite his logic, he has a strong, well-developed Fe that he uses to empathize deeply with others and build his moral framework off of. His goal is to explore the world, but he cannot and will not sit idly by when people are having their freedoms taken away. Nonetheless, above all, his goal is to understand: Everything, everywhere, all at once. He wants to understand it all, including people. And to some extent, he does. Or at least tries to. He fails often in the face of irrationality, but that only makes him want to figure it out even more. And eventually, with the right person (who also happens to be INTP!), he gets through to them.
\Please do not argue with me about him being an INFJ. He's not. PDB sees someone who has empathy and morals and assumes they MUST be INFJ. There's a lot of mistyped INTPs on there.)