Some legal definitions taken from the Citizens' Advice website (stress added by me):
"The police and Crown Prosecution Service have agreed a common definition of hate incidents.
They say something is a hate incident if the victim or anyone else think[i it was motivated by [i]hostility or prejudice] based on one of the following things:
disability race religion transgender identity sexual orientation."
"When hate incidents become criminal offences they are known as hate crimes. A criminal offence is something which breaks the law of the land.
Any[i criminal offence can be a hate crime if it was carried out because of [i]hostility or prejudice] based on disability, race, religion, transgender identity or sexual orientation...
Here are examples of hate crimes:
...causing harassment, alarm or distress (Public Order Act 1986)."
A (small P) pedant like me might observe, firstly, that the interpretation of "hate incidents" is totally subjective, and, secondly, that the terms "alarm" and "distress" allow more elasticity in the interpretation of what constitutes a "hate crime" than you you might hope for in well-formulated law.
Nonetheless, these definitions are, I guess, the intended standard by which Facebook etc will exercise their duty as proxy censors.