1984 of course someone's right to earn a living is not less firmly entrenched if they are in the public eye, or highly paid, or both. No one is saying that.
However, everyone knows that one can't treat one's work email like one's private email, especially if it is also copied into someone who may find the contents of the email offensive - so he fucked up. In some firms it could lead to disciplinary action.
On top of this he is supposed to promote an end to sexual discrimination within football. His casual dismissal of women within these emails does suggest a lack of sincerity on his part in this matter. This would lead to questions about his suitability to perform this role in genuine good faith.
Finally people have been sacked for making racist remarks when they thought they were in private. I actually fail to see why this is much different.
Yes private banter however much in poor taste or offensive is completely ok, but this wasn't private.
If he had said these comments out loud with the PA in this room, which led to her feeling awkward, do you think she would have cause for complaint?