Oh gosh, I’m so pleased you liked my little bit of meta! (I just went back and re-read it to refresh myself on what I said, lol). And this is a really fascinating question!

I think to start you’d have to list their flaws. 

Newt: selfish (I’m a doctor!), self-centered (making Hermann’s lab life miserable with the entrails, the Drift experiment being partially out of desire for attention and to be right), messy (Kaiju entrails), maybe a bit shallow (with his fashion sense and body art), un-empathetic (talks about how cool Kaiju are around people who have lost family to the Kaiju), often deliberately obnoxious (literally everything with Hermann), hyperactive and screechy (Charlie Day), immature (in many senses, but also in his fanboy qualities), Down to Fight at all times (“Is it impossible?!”), can’t keep a secret ( “… I’m gonna tell you.”), reckless and impulsive (the Kaiju Drift), arrogant and wants to be the center of attention (I mean…  basically everything about him). Obviously he has many virtues which I’ve described elsewhere, but that’s not the point of this post.

Hermann: cantankerous (he’s 36 going on 80),  a busy body with his nose in other people’s business (“Please excuse him, he’s a Kaiju grrrrroupie.”), spiteful (it may not be on purpose but he kicks water at Newt in their very first scene, and just in general this is true of him), smug (about how Newt is wrong), arrogant (literally everything about how he puts down Newt and his theories), dismissive (“Politics, poetry, these are lies.”), impatient with others (though that could just be Newt, who could drive anyone to madness), cold (at least outwardly towards Newt, many of his insults cut close to the bone), authoritarian (Hermann appeals to military authority and clearly admires it) and just all around difficult to deal with. Interestingly, many of these traits are gone by Uprising, while “Newt” gets a whole new batch of very different flaws. And again it should be stressed, Hermann has many virtues including but not limited to his intellect, his determination, his drive, his raw courage, and his persistence in the face of dismissal, discomfort, and disability. 

And by the way, both of them think they’re the “normal” one who needs to look out for their obnoxious colleague and I just cannot with them they are both heinously difficult human beings in the best way lol. 

And now onto how the Newmann ship would deal with these flaws:

I think a lot of how Newt and Hermann would deal with one another’s flaws is that they have been dealing with them for years now already. These flaws are not new or shocking to them, nor have they driven the other away. Clearly, they tolerate one another when anyone else would have withdrawn to a safe distance or just abandoned them entirely. They clearly care for each other in spite of if not because of these flaws. Even pre-Drift they try to protect one another from their most dangerous fascinations (Newt his obsession with the Kaiju, Hermann his attraction to the military). 

Clearly they have flaws that do genuinely drive the other to distraction. Newt seems genuinely upset when Hermann dismisses his theory and his findings regarding the Kaiju Drift. But on Hermann’s side, the proposal of that Drift seems to have genuinely touched a nerve of fear on Newt’s behalf that he covers up with snideness and dismissal.

I’ve always gone with the theory that it’s more their method of communication with one another that was clashing. Hermann didn’t understand Newt’s obnoxiousness towards him was the equivalent of pulling pigtails, that Newt wanted Hermann’s attention and regard. Newt couldn’t understand that Hermann’s dismissal of Newt’s obsessions was his way of trying to protect Newt. It’s one reason I think the Drift fused them into a functional whole after so many years of clashing, it finally showed them through a direct mind connection what they had failed to communicate. All the times they had been sincere when the other thought they were joking, and vice versa. Their method of communication. Their respect for one another hidden beneath a prickly surface. The way they’d both tried to hide their vulnerabilities from one another and thus both come off as distant, cold, and uncaring to one another. I have no doubt that the “instant hatred” at that first meeting after the letters was because both of them had such high expectations but didn’t know how to communicate with one another outside of written format where everything could be cleanly expressed.

That said, I think that before and after the Drift they actually do love one another for their “flaws”. I think Newt and Hermann are both heinously arrogant when it comes to their intelligence and their field, and I think they love that about one another, albeit secretly at first, or perhaps rather what that arrogance is a result of and how it translates. They’re both tops of their field, poised on the eccentric edge of it, they’re both the very best at what they do, and I don’t think either of their personalities could stand to be around someone who wasn’t on their level intellectually, or someone who tried to be modest about those accomplishments.

I think Hermann’s busy-bodyness is one way that Newt knows he cares. Newt would be at a genuine loss if Hermann stopped poking his nose in, as a sign that he’d stopped caring. Likewise, if Newt stopped being deliberately obnoxious to Hermann it would mean the same thing: apathy would be far worse than needling. Hermann probably wouldn’t know what to do with himself. There’s a compelling case to be made that the sniping serves a dual purpose in these final days of war which is to keep both of them from having a screaming breakdown over the stress and the sheer unholy knowledge of how fucked the world is, so when they’re bitching about little arguments and annoyances they’re not thinking about the void that’s about to open up beneath their feet.

I think Newt’s hyperactivity and fanboy qualities and general devil-may-care attitude is refreshing for Hermann and his authoritarian upbringing. I think on his own Hermann would retreat into an isolation he’d verbally claim he prefers but which would eat away at him. He may gripe about it, but he thrives and seeks Newt pulling him out of himself. Likewise I think Newt is always seeking validation. By being such a difficult person who doesn’t flatter others easily, Hermann’s regard is worth that much more and it could serve as a grounding influence on Newt to know there’s someone out there who sticks by him and engages him intellectually, even if they don’t always agree (they don’t need to agree if it’s a matter of intellectual debate). Even when arguing, Hermann validates Newt by never dismissing him from his presence or truly giving up on him, another reason the dismissal of the Kaiju Drift clearly is hurtful and unexpected to Newt (who can’t read it as a protective action). 

They call one another on their bullshit. They’re not personalities who need to be coddled or told they’re right all the time or flattered. They might respond initially to flattery, and even get puffed up about it and smugly rub it in the other’s face, but it would wear thin. They’d realize the thrill and rush of flattery is dissatisfying. That they’d rather earn the other’s aggressive debate than the fawning of lesser minds. Even when Newt is showing off to Hannibal Chau it’s because he clearly identifies an equal in his field, albeit a black hat to his white hat, a criminal to his academic. They want to impress equals and they serve as equals to one another. 

I think anything beyond this would go well into fanon speculation. The last note I’d say on Uprising, because they become such different characters there, is that clearly Hermann is stunned when Newt won’t help him. Clearly in PR1 Newt is stunned when Hermann won’t back him up that the Drift worked when it clearly did. That tells me that even at their lowest, they supported one another, even if they might grumble about it. The grumbling is half the fun.