My sufferer worked in probably one of the worst fields to work in with PTSD - he was a correctional officer. The atmosphere is incredibly clannish and clique-filled, and there are a lot of factions, some who are in the good graces of the higher-ups (usually the warden and those just under and above the warden), and those who are not, along with those who are in with the union reps, those who were put there (in that particular prison or position) by their cronies, and those who, like my sufferer, were kind of outsiders to any of the factions. The politicking was unbearable to ME and I didn't even work there. I couldn't imagine what a pain in the ass it was for someone there.
That said, he found it best to just not form many friendships within his workplace. He had a few friends at the prison itself, some within the wider system (parole officers and at other prisons), and the majority of his friends had nothing to do with the system at all. He kept his head down and did his job. He was well-liked as a supervisor, because he DIDN'T play politics and was fair with his workers.
He was not well-liked by his superiors for the same reason, and he felt, as well, that he was discriminated against for many reasons. On one hand, he was. He was not going to promote any higher than he was because he didn't play politics.
On the other, I was approached by his coworkers (the ones he did get along with) throughout the years who basically told me it was his attitude that had him isolated. Those who got to know him ended up friendly, but getting to know him was almost impossible. He wanted to make friends sometimes, but it had to be on his terms and his terms alone (he would not go out with them, wouldn't join in the various baseball/golf/softball/bowling leagues they had, etc). If he WAS invited to do something that he had no direct interest in, he refused, and they stopped trying. If he invited someone else to do something, he would not compromise to any of the details, and generally bailed anyway.
Through it all? He thought he was being reasonable, friendly, approachable, and was confused as to why "no one" liked him (but at the same time claimed to not care). He had friends who truly cared about him, but most of them did so from a distance. His anger at being punished for not playing politics came through more than he realized, and it did not make it easy for people to accept him.
Ironically, this job seemed to "work" for him, and he was at it for quite awhile. I think my advice for someone with PTSD in finding a job that works, is probably the same as for anybody: If you aren't embraced by your coworkers, make sure you play by the rules so they don't have a reason to get rid of you just because you don't fit in. Find friendships and fulfillment outside the workplace. And, if it's a consistent problem with not being liked by coworkers...look inward.
It may not be your fault, but, especially with the issues that come with PTSD (hyperviligance, distrust, emotional distance, etc), it's very easy for others to pick up on that quickly, but if they don't know the reason, will just see you as stand off-ish or unfriendly. It was (and continues to be) a major problem for my sufferer - he hates that people "assign" emotions to him...and he doesn't realize that, to someone who doesn't have PTSD, if you look angry and act angry, they will figure you are angry. If you constantly refuse to join in, they will stop asking (and, at least for my sufferer, he would ignore or not remember the offer to begin with, or even resent the offer because it came from the people who he looked down on for politicking).
Anyway, sorry if that was too long. I am definitely not trying to be critical, and I can't imagine trying to navigate the petty crap that goes with working in any environment, with PTSD. I have no idea of the situation of your sufferer, beyond what you've provided, so it may not correlate at all with my sufferer's experience. I am probably rare in that I DID have the "other side" PoV as well (coworkers that approached me).