The Cleopatra quote is talking about individuals; Individuals which we know make up a group, but individuals nonetheless.

“Anyone” is a similar concept. You talk about a single person(it’s right there in the word) and apply that condition to however many people. An example in a group of all men would be “anyone may leave the room if he so chooses” and even though it sounds weird, because we heavily favour the singular they, it absolutely works.

This has strong “everything is a conspiracy when you don’t understand how anything works” vibes. Your lack of understanding shouldn’t have to be everyone else’s problem.

So you would say that when referencing a singular specific person of undeterminate gender in the third person we should use is? Because I am quite sure that, if that has ever been correct at all, it certainly isn't now. As per merriam webster: A student was found with a knife and a BB gun in their backpack Monday, district spokeswoman Renee Murphy confirmed. The student, whose name has not been released, will be disciplined according to district policies, Murphy said. They also face charges from outside law enforcement, she said.— Olivia Krauth

E: also, "Each member [of the women's touch football team] found something they could improve on in the future."

Dalby (Queensland) Herald (Nexis) 21 October 16, 2014 (as quoted in the oxford english dictionary)

Contradicts you as well unless you'd like to argue that "each man are fighting for himself" is correct.