Is it acceptable to ask for the original bibtex file of a paper?

I would consider this a perfectly reasonable, if unusual, request.

That probably has a lot to do with the culture of my field; most papers in particle physics are uploaded to arXiv as LaTeX source (though .bib files are often not included), which is then made available to download along with the rendered PDF. This facilitates a cultural expectation that source code to the paper should be available to readers, not hidden. So I would consider sharing the BibTeX file associated with a paper to be a reasonable thing to do, a professional courtesy of sorts - similar to what sharing a copy of the paper itself is or used to be.

Other fields may think differently. Still, in most cases I would think it's fine to ask. The author can always say no or ignore your request, if they don't want their file to be shared for some reason.

My feeling about this is that if you don't personally know the author, it's weird and tacky and will probably result in being ignored. Even if you do personally know the author, it's still kind of weird and tacky. But there's nothing unethical about it.

As an alternative solution, if your institution has access to Scopus, you can find the paper there and see the citation list and export it in Bibtex. Web of Science has a similar feature.

To answer your question, however, it is not really unethical, but would likely be seen as a weird request.