I just went and did my errands
That, in my experience as (former) supporter of someone with a high degree of double standards (and the corresponding bed linen and a whole lot of other stuff), is probably the best thing to have done, for you. I can't even tell you how often I "just went" and let it go. Maybe it is another matter of finding out for oneself whether this is a battle worth fighting, or not. Which leads to...
double standards, NOT the issue of bed linen or anything else
I think it IS an issue of bed linen (to take this example you gave, but which is, of course, exchangeable by so many other things) AND double standards at the same time. It IS double standards, and at the same time, if it is double standards AND something generally not important (as is bed linens), I guess one should ask whether or not one (you yourself) needs the stress of fighting for this. I think it is difficult to discuss something with someone (non-PTSD but even more so with PTSD (or other disorders with similar/the same symptoms) generally (double standards) with a specific example (bed linens) in mind. It can be difficult for some people to focus on the bigger picture (double standards) when throwing a specific example into the whole discussion.
There are two things that came to mind when reading the thread:
1. My very first therapist said to me once not to worry about "their" (at the time my sufferer's) tantrums and all. It is them that they embarrass, not you. They are adults and if they have a fit or a tantrum in public, they embarrass themselves, not you, as people outside of your relationship realise that you're not responsible for another adult.
2. Could it be denial? Could it be not primarily about double standards or bed linens but rather about wanting to get a result that just isn't there, no matter how much you might long for it to be? In my own experience, once you've gotten rid of denial, "hoping for the best but expecting the worst", you may end up at the question: Do I really want to fight this battle? Is it worth it for me, considering what "the worst" may be?
I just read "The PTSD Relationship" by PhD Diane England and they basically said the same thing. It opened my eyes about many things, from one perspective (supporter) and the other (sufferer) and, most valuable for me personally, both together (entwined).
Have you tried the exercises in the book? I remember one that could be very relevant but just looked and couldn't find it on the Kindle.
Having said this though, and going back to me being the supporter, I think what it was with me was denial. It just sucks BIG TIME when you find that things just never seem to truly change, that you seem to be able to change only the now and yourself/your own actions in the now. I am really sorry if you feel that way.