Other then that, Iger frequently works with people with whom he disagrees politically. Much of the criticism of Iger is that he's a soulless, impersonal business automaton. He makes decisions to make money.
The idea Musk embarrassed Iger is absurd. Iger is far more self-confident then Musk and realizes that his little tantrum made Musk look like a tiny little man to anyone who wasn't already a Musk sycophant.
I think this view of Iger has largely been discredited over the last few years. Just recently in this press we have learned a number of unflattering details about Bob Iger's emotional maturity. Examples include...
1) Iger was horrified that his successor lost his temper and said a curse word
2) He was offended when Chapek wanted to study by himself instead of preparing together for a shareholder presentation (talk about neediness)
3) Iger lashed out at Chapek for scheduling a routine meeting with the CFO
4) He was hurt that Chapek didn't revere him enough
5) He worked to topple his chosen successor through subversive and ultimately cowardly means
Iger once, rather ironically, lashed out at Disney Parks fans on Twitter. In a bizarre Tweet in the aftermath of insulting Expedition Everest, Iger jabbed at the company's devoted fanbase:
Because it's funny to mock people who are concerned with the declining quality of projects and toonification of the theme parks. It's a good thing he didn't move forward with his plan, given the abysmal box office performance of The Marvels.
The entire concept of "Disney Nice" that he has embraced as his corporate culture is an example of emotional immaturity. It's clear from information about the Chapek debacle, that the executive team struggles to speak boldly and directly to one another. This results in passive-aggressiveness and petty backstabbing. Again, ironic, because Walt Disney was not afraid to speak bluntly and directly to his subordinates. And stories from Walt Disney Productions make it clear that the company culture had a high level of accountability. And Iger's idol Steve Jobs also was known to be... Direct.
And then there was the self-congratulatory Masterclass series he did. And the "Ride of a Lifetime." And other projects to specifically pump up his legacy and ego.
Admittedly, Elon Musk might be one of the most emotionally erratic business leaders I've ever seen. He can be extremely impulsive. Sometimes the impulses can be genius, and other times moronic. But let's not kid ourselves and think Iger is a machveiallian business leader. He's shown time and again his own different emotional immaturity.
Edit: I'll add, the reason he got the reputation as the "soulless businessman only out for money" was his disregard for the parks. I think the truth is he just didn't really care about the parks. If you don't care about something (except for Shanghai Disney and the Galaxies Edge which are monuments to Igerness), you can leave that to the accountants and MBAs to run. And they were the ones who were the soulless businessmen extracting every cent out of the park. That or they are just incompetent.