By correct, in this context, I mostly meant English (especially American English) style guides and similar that were published over a number of decades prior to maybe ten years or so ago. I'm sure there are lots of individual examples that don't follow that timeline though.
After people started to become more generally sensitive to gender role assumptions and language that reinforced those assumptions, I can recall lots of examples of "he/she" constructions and/or writing examples in a way that you had both a male engineer and a female engineer.
The preference for using singular they in part because it doesn't still rely on binary pronouns is relatively recent in my personal experience--at least in formal writing.
After people started to become more generally sensitive to gender role assumptions and language that reinforced those assumptions, I can recall lots of examples of "he/she" constructions and/or writing examples in a way that you had both a male engineer and a female engineer.
The preference for using singular they in part because it doesn't still rely on binary pronouns is relatively recent in my personal experience--at least in formal writing.