Ever heard that inside every type is their shadow type or something along those lines? Like, an INTP has an ESFJ inside of them that comes out when they're stressed. That can be rather true. I'll explain myself for a good example, mostly because I've been obsessively trying to type myself for ages and think I finally solved the puzzle and might as well share.
So, I recently figured out (or am pretty sure I have) I'm a really unhealthily developed INTP. For a while I thought INFJ and seriously considered ISFJ but my friends were like 'no, I really don't think you're a feeler.' I pretty much analyzed every piece of data I could, thought of all the possible possibilities I could generate. (Within reason. I kind of left out all the XSXP types as I have NOOOO Se.)
I realized INFJ was not fitting well about a few weeks ago when it kept coming up that I'm way too critical, blunt and have way too much of a struggle with comforting people (as in, I tend to give advice instead of comfort) for that. So, the first thought was 'maybe, INTP, I'm pretty sure I have Fe and Ti.' Back then I was certain I had a rather strong Fe. But the logical-ness of the INTP seemed so weird with the fact that I am emotional (though, not particularly emotionally driven, I've found) and fussy. What further got me bent out of shape is that I was utterly convinced I have an NF bent because I have such humanitarian interests. (Though, to be fair, I seem much more interested in learning/thinking about and understanding social issues than I am in becoming an activist. )
So... I tried to think of every other possibility and obsessively exhausted all of them. The two others I almost settled on were INFP and ESFJ/ISFJ. INFP basically didn't work because I have a very obvious Ti and my friend (INTJ) who happens to have a ton of INFP friends was all like 'yeah, no, you do not have Fi' and I had to concede to that after she gave me her reasoning. [In fact, she was the first person who was utterly convinced I was an NT type (specifically an INTP)]. So, I thought maybe ISFJ and superficially it almost fit. But...
In the end, I realized that the worse my mood is, the more I try to be like an ISFJ. The key word here is try. It comes off as rather forced an unnatural. I've basically had people tell me it's like I force myself to be accommodating when I'd rather rip out and critique things. That when I let go, I'm really more blunt and logical than anything else. I get fussy and rule stickler-y and lost in the past... but only when I'm completely freaked out.
As a kid, I was this heads in the clouds little thing, always off in my dream world of Ne possibilities or building my own realities. I was harsh and critical and really liked to speak my mind. Rules, authority, being proper and all that meant diddly-squat to me.
So... what changed? Three things had a major influence on how I developed. The first is that I was really horribly bullied all the way up to high school and in high school, I was still 'that weird' girl. It made me feel pretty isolated and like there's something wrong with me. Like being who I am is not okay. The second is my parents. I'll save you the gory details and sum it up in that we have this horrible relationship that borders on abusive with them. They basically confirmed everything my peers said. "Yeah, people don't like you because you're weird. You need to work on your social skills." And while I probably did (and really still do) need to work on my social skills, hearing that from my parents really wasn't helpful. The third is really a mix between anxiety and insecurity. I have clinical anxiety and well, I'm pretty sure I'm an enneagram type 5. (I'm still figuring out the wing.) My biggest fear is being incompetent. Which manifests in a lot of ways, but in relation to this, I feel very socially incompetent.
So, what did I do? Well, there was one, dark, dark year in middle school where I said 'fuck the world, I'll be whoever I want to be.' And I was this self centered jerk who only followed my own rules (ex. I refused to turn in homework because it was too easy and therefor I was above doing it) and basically was highly unpleasant, though pretty creatively productive. I did end up meeting my best friend, an INFP, who kind of, oddly enough, helped ground me and pretty much kept my more insensitive traits in check. (He's still my main social anchor.)
After a few years of working through things, I tried to morph myself (mostly subconsciously) into someone likable, falling back on my inferior functions. I still stayed very imaginative, idea and abstract concept focus and analytical... but I became a bit of a rule and social norms stickler (or tried to be. I'm still not very good at recognizing them, though I am rather good at following recipes). I also tried to learn to listen better, learn to be more accommodating. And it kind of worked.
Sounds almost healthy, right? Except... well, I'm behaving in a way that's really counter-intuitive to me. It's taxing and stressful and actually makes me more insecure. Like my friends tell me, I try and force myself to be accommodating. I personally notice myself getting so lost in rules and social propriety that I'm afraid to do anything. The only place I really am me is in an academic or creative environment (I'm a math major who does art and writes as a hobby). That's where I analyze things, generate ideas, problem solve, all the lovely stuff that makes me feel like -me-/get pumped up.
But outside of that realm I'm so paralyzed with fear and insecurity that I become utterly ineffective or utterly annoying.
Basically... an unhealthy INTP can look like a kind of underdeveloped ESFJ/ISFJ (fussy and rule stickler-y without the tactful and responsible side).
Si and Fe are very valuable tools when not used as a fallback. My Si sometimes really feeds in well with my Ne when I'm in creative mode, helping me recall the data and facts I need as inspiration to generate ideas and concepts or when I'm trying to analyze things. And Fe is great for being able to emphasize with people... I actually kind of wish mine was better developed because it would be rather nice to actually be aware of appropriate social behavior rather than constantly having to ask 'is what I'm doing appropriate????' and feeling unsure.
I'm still trying to figure out how really address this imbalance as my inferior function are rather naively developed but overused. Mostly, I'd love it if my Si would pop as a memory/fact check function and help me keep track of things instead of popping up as a 'noooo, you can't do this, it's dangerous!!!' function more often.
....
On a less detailed note, I would like to add that I'm pretty sure INTPs can also go the opposite way, completely ignoring their inferior functions. At least, I've kind of observed a trend among rationals where we tend to be VERY critical of sensors and feelers. To the point of completely dismissing any good traits S-types and F-types have and to the point of dismissing how useful and applicable the Se/Si and Fe/Fi functions are. It can manifest in being very egotistical, very callus, very overall ass-holey. Which is annoying on it's own, but it's also crippling.
For example, an INTP without a good use of Si can still come up with really great ideas and systems... but those systems won't have any sort of grounding. Without a memory bank of facts to build off of, and INTP can get stuck or come up with way off ideas.
Rationals in general can get what I would dub a intellectual-superiority-boner. We can think we know everything soooooo much better than everyone else and kind of mentally jack off to it and not realize just how stupid we are. Or use our smarts as kind of a 'well, I'm smart so I'm important,' crutch.
There're also rationals who subscribe to 'logical' ideologies without really considering if they are logical or just ideologies that scorn emotion/less rational things. Ex. I have a huge problem with mainstream atheists for this reason, and I say this as an atheist. A lot of them just flat out condemn religion and uphold science in an almost religious way, forgetting that science is very much influenced by the society in which it originates. (You have to look no further than Eugenics movement to see how ridiculously bias science can be). However, a lot of rationals identify strongly with mainstream atheists.
Basically, another unhealthy way INTPs and rationals in general could go is trying to be so rational that they actually become irrational.
....
But, these later things are just my musings. The people I spend the most time with are two INFPs, an INTJ, an ISFJ and an ENTJ, so I can't really speak for INTPs other than my rather strangely developed self. (Though, if I don't sound very INTP here, feel free to say so. It seemed like the most reasonable conclusion to reach, but hey, typing is confusing and complicated sometimes. )