Why would a free speech absolutist fire people for using their free speech?

Saying free-speech principles are important in the public square, which he asserts Twitter et al are part of, is very different from tolerating all forms of speech from your own employees in the context of their job.

He claimed to be a free speech absolutist, not a supporter of free speech principles. I chose to read that as a highly intelligent person using the words he wants to use to describe his position accurately, I also expect him to live by that position given he has the means to do so.

There will always be some excuse why the speech he doesn't like is different, and not subject to his supposed priciples.

Yup. “But my abortion is different.”

Has Musk ever said that employers should tolerate all speech from their own employees?

I guess if they singed it out of key, he might have to

I'm worried they might have got their fingers burnt!