Having read the book, it doesn't read out of place at all. He makes similar disparaging remarks to other groups. He even calls developers & hackers animals in the title. This is the overall tone the book is written in, he doesn't single out women for a particular rant. I'm sure it seems that way when all you read is a short quote. The notion that this except is a clear indicator that Antonio will inevitably harass, discriminate, or otherwise do something that gives good cause to avoid employing him is a long stretch.
The real answer, were I Antonio's boss, is that I'd talk to him and see what his views really are. I'd ask around and see if he's treated women poorly.
There is a lot of people with stupid ideas in the world. You cannot punish them all just for their ideas.
In particular, he made a bunch of statements which would make me concerned about him being in any sort of managerial role over women. He doesn't seem to have tried to walk them back or show some sort of change of heart (or "c'mon guys, it was all just a bit"), so I think his almost-coworkers had a point when they started that petition against him.
People's ideas do matter. Ideally misogynists should not be in charge of women.
Everyone has a right to work (irrespective of position), to live freely, own property, etc..
Justifying the opposite because of someone's ideas is a very slippery slope. And the fact that politics is a game of perception makes it all the more dangerous. If the mob rules, the true rulers are the people who control the mob (an even smaller amount of people)