Further it seems that West Yorkshire Police has no knowledge of the civil law ...
This is fair enough. Their job is to prevent, detect and investigate crime, catch criminals etc. I'd expect them to have a good working knowledge of criminal law but there's no reason to expect anyone outside of HR to have an in depth knowledge of the EA or any other area of civil law.
The woman was contacted because of a complaint of malicious communication. She'll have been given 'advice' based on hate crime legislation and its farty little brother 'hate incident' (not sure if this is law or guidance) - these all come under criminal law, not civil law.
Nevertheless, all police officers should have a basic understanding of the EA because they provide a public function so are themselves bound by it in the way they treat the public.
The woman might possibly have a discriminatory harassment case against them if she can show the police created an intimidating, hostile, degrading, humiliating or offensive environment for her because of her sex (section 26 - harassment). This would be difficult because they have also treated Harry the Owl just as shittily.
That would be a civil case though, she'd have to make a complaint to IPCC or use the civil court procedure.