The former Manchester City and England midfielder, who remains without a job following his sacking by Bristol Rovers in October, openly delivered his controversial views on social media.
But the Chelsea boss took time out of her pre-match press conference to give a measured and incisive response to the issues raised by Barton, who claims to be taking on a "woke agenda".
“The realities are male privilege is something that has always been at the centre of women’s football in this country," Hayes said. "Women were banned from playing football up until the 70s.
"I don’t expect any individual personality to understand their privilege — nonetheless, you only have to see scores of women on the internet, whether a presenter, coach or player, to realise we are routinely used to dealing with systemic misogyny, bullying and behaviour which is pretty normal for a large part of the football public.
"The realities are that I find the debate interesting; we should have the debate without being personal, and I am not referring to any individuals.
Barton claimed that "women shouldn't be talking with any authority in the men's game; come on, let's be serious, it is a completely different game." Hayes however was keen not to respond to his comments directly.
She preferred to speak more generally on the subject, adding: "I feel that sport is probably the last place in society where that male privilege exists, so, if I go all Darwinism on us and speak on evolutionary theory, when there is an existential threat, you either evolve or die. It is one or the other.
"And when it comes to the sport of football in this case, we have to remember society isn’t always well represented across coaching or the media.
"And if you haven’t experienced systemic misogyny like many of us have, then you can’t understand how detrimental these conversations are, knowing that anything anyone says just enables an absolute pile-on, particularly on social media, which it doesn’t take a lot for people to pile on, to do that is pretty normal for a lot of people who support football.
"And so, it is sad, a little bit, not that we are having the conversation as we should have a conversation about the broader issue.
"Rarely do we go into a hospital with a female physician who might be carrying out surgery on a kidney; we won’t turn around and ask if she’s was a good patient once.
"We know being a good patient doesn’t make you a good doctor - you just need a talent and a skillset. It’s the same about being a great banker. Do you have to be a frugal spender to be a good banker? A well-travelled passenger to be a good pilot?
"We become so unaware of our confirmation biases, but also when there is an existential threat, then what we do to make ourselves relevant is to create a lot of noise around a topic, but we can do it better in another way."
In terms of matters on the pitch, Chelsea have Melanie Leupolz and Guro Reiten back from injury, but Millie Bright and Jelena Cankovic are out for the trip to the Emirates Stadium, where 53,000 seats are sold with two days to go. The Blues have sold the away end out.