Did this email cost Mailchimp's billionaire CEO his job?

Probably not, if this is the reason you fire your ceo then you probably wanted to fire him anyway

They probably have a layoff coming which is closer to 50% than to 10%. Does he want to be the one who does it? Probably not. Does Intuit need another CEO floating around? Probably not. He pretty clearly feels not much meaningful work is happening if everyone is focused on politics.

Does a mail platform need that many people? Look at the economy. It is related to this email sure, specifically it is related to his opinion on how engaged and productive staff are being.

I don’t get how somebody in his position would think they could make transphobic comments without repercussions.

There's nothing transphobic in his email.