That's not how language works. The word "manufacture"? It literally means "made by hand." When we created factories to make things for us, we adapted the existing word. "Ambulance"? They
walked for those who couldn't because they were first stretchers that others carried. We added wheels, then an internal combustion engine, and we went on using the same word.
"Internet" is a notable exception in my lifetime. It usually requires some kind of huge invention or discovery for that to happen. "Manufacture" is far more the norm.
While the use of the singular "they" as applied to people who are non-binary is relatively recent,
its use has existed for about 650 years, at least.
We use it all the time in sentences like, "Did every
one remember
their toothbrush?"