Hopkins rowed with former MP Edwina Currie and sparked outrage on Twitter for her comments as she claimed that woman "couldn't handle" equality.
The panel on the BBC One politics show were asked if Keys and Gray's firing was appropriate following their sexist remarks about assistant referee Sian Massey.
"I think Sky Sports has completely lost its sense of humour. I think as a nation potentially we have lost our collective sense of humour," Hopkins told the studio audience.
"I think people like Karren Brady, who have appointed herself patron saint of all things equal, does not speak on behalf of all of the sisterhood. I think women actually don't want equal treatment, they couldn't handle it if they got it, quite a number of them. It's a tough world out there."
She continued: "What a lot of women are actually asking for - and you can look aghast at this - is special treatment. If you look at all female shortlists for positions, is that equal treatment or is that special treatment?
"I think what women need to realise is that you have to toughen up, we can't ask for equal pay, you have to be paid on performance and the results you deliver. It's a tough world out there and I don't think Karren Brady or any others are doing us any favours by putting this sort of debate out there. I think we have to just compete in what is a tough world.
"And finally, I think the art of banter is something we should be proud of as a nation. I worked for a while in the military and our forces, the best in the world, in my opinion, they survive in banter. I think we need to keep that, we need to look after it."
Hopkins also added that nobody was interested in watching women's football and that people would not pay to watch it.
Writer Grace Dent mocked Hopkins's efforts on the show, writing on Twitter: "How do you get on Question Time when you're as thick as Katie Hopkins? Do they just search the web for trolls and send a minicab?"
Meanwhile, fellow Apprentice contestant Stuart Baggs joked: "Loving how Katie Hopkins pauses for applause once she's finished speaking -awkward!"