(Oh boy, my special interest arises once again. Long post with links coming.)
It IS acceptable by and large and not appropriative unless you are otherwise acting badly. Claiming to be doing it “more correctly” than the established traditions, performing hijab “tourism” that’s meant to “learn what they go through,” or taking a very specific style that’s not from your history (IE Gele or similar, which are very specifically African styles) would be the problem.
A couple Muslim sources online and one Jewish one (Rivka Malka) I have on hand are all openly fine with non-Muslims doing so if that’s what feels good to them. To put it plainly, many of them feel that modesty does not belong to one culture and headcovering is an act of modesty. If you’re not Muslim, it’s not hijab because hijab is specifically their code of conduct. If you’re not Jewish, it’s not tznius because tznius is specifically their code of conduct – but it’s the same idea.
Headcovering pre-dates monotheism (even Jewish monotheism, because that didn’t actually occur until CE – Judaism existed, it was not monotheist them.) The main sources we have that confirm this are Roman. It was, although I don’t have this source on me, a way for upperclass Roman woman to leave the house when such an act was seen as a threat to family honour and integrity.
Headcovering was also present in Norse culture at various times, including the period when Christianity wasn’t omnipresent in Europe. For the most part, as far as I’ve gleaned from doing extensive research on it, headcovering is simply practical. It’s protective from sun, sand, cold, and wet. It maintains your hair when such care was likely labour intensive. It’s a very easy way to distinguish between different people, genders, or social classes. Prostitutes in Rome were forbidden from wearing headscarves. Likely other cultures before Rome did it as well, but we have less certain sources on it. Egypt did wigs, we know, but not necessarily about scarves for daily wear.
It has likely existed for most of human history since we started wearing more elaborate clothing, and quite frankly there’s only so many ways to attach a strip of cloth to your head.
Most pagans I’ve seen talking about headcovering are either doing it as a devotional act, as a way to keep their hair or head covered to conserve power or block outside energy, or simply as a means of privacy for personal or marital reasons. For myself, at this point, headcovering is secular and always has been – it’s privacy, care for my hair, weight/pressure for anxiety. There’s as many reasons to cover as there are ways to cover.
A lot of people have internalized the idea that “only Islam covers” which is I’d say an aspect of orientalism and islamophobia. At the turn of the 20th century, most of Christian Europe was still covering too. Only after the Iranian Revolution did headscarves seem to unilaterally signify Islam, and it’s unfair and othering to persist in that, in my opinion. (”A Quiet Revolution” by Leila Ahmed discusses some of this.)
If someone wants to cover, I’d highly suggest they do this kind of research to determine what your own opinion is. You can obviously tell what mine was, and I developed it after being challenged on the point. I love covering. It’s just part of my life now, but I remain aware that challenges about appropriation are to be expected.
If you’re wearing a scarf that can be mistaken for hijab, you really might want to also be able to answer questions about Islam. (I’ve gotten into a 40 minute debate about the Qur’an being “awful to women” because of this.) I consider that to be the debt you pay for bringing covering out of being “only Islam.” You owe ALL people who cover that respect, or frankly you shouldn’t be wearing it.
Obviously if you have any other questions, feel free to ask.