Milk
that beast? Pull the udder one!
It just struck me, in English there isn't a non-gendered singular name for one of those animals:
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The answer to that question is probably best found in a reference that uses "kine" rather than "cattle" for the plural. Alas my copy of HHH is in a box in the office presently, I'm sure he has a section on such animal words. /Language history, language change, and language relationship: An introduction to historical and comparative linguistics/
https://www.degruyter.com/document/doi/10.1515/9783110613285/html . Highly recommended as an introductory text for those who got a taste for the field through people like Crystal or Bryson, but found their morsels a bit too mignon.
Given that the PIE *ghou has evolved into words that now imply non-gendered, male, and female varieties of the animal, it doesn't seems obvious that gendering was the most important thing on people's minds when they were adopting the word, else the gender would have been preserved better.
Explicitly:
PIE. "*ghou" > (missing links) > L. "bos" > O. Fr. "buef" > Eng. "beef", where the modern French "boeuf" is gendered male (in contrast to their female "vache").
PIE. "*ghou" > (missing links) > Proto-Germ. "*kwon" > one of the germanic languages "Kuo"/"ku"/etc. > O.Eng./M.Eng. "cu" > Eng. "cow" now gendered female.
Who knows where along those chains/trees gendering was introduced, it could be in the leaf nodes, as there's no reason to rule out a spontanious symmetry breaking where the separate languages influenced each other *after* splitting.
(For completeness, arguably PIE. "*ghou" > ... > Eng. "buffalo", gendered neutral, too; so all three bases are now covered. However, that derivation is sketchier.)
(All etymologies ultimately synthesised from
https://www.etymonline.com/word/*gwou- and the obvious links therefrom.)
But that doesn't answer your question - what word should be used for a non-gendered domesticated bovine? You already have your answer...
I think it's generally agreed that the stall animal being referred to in Chaucer's /Truth/ (the poem where the phrase "the truth shall set you free" comes from) is a cow - and he was a very learned man familiar with a wide range of animal words - but notice his word choice: "Forth, pylgryme, forth! forth, beste, out of thi stal!". A curious side note - this poem is being addressed to a lord with the name "Vache" ("Therfore, thou Vache, leve thine olde wrechednesse;"
https://www.poetryfoundation.org/poems/43940/truth-56d222d5bf80c - that 4th stanza isn't part of the poem, it's an "envoy", a postscript to accompany the poem itself).
So, if in doubt, just call everything a "beast". If it's good enough for Chaucer, it's good enough for all of us.