No I think their response exactly matched my theory.
They're just doing and saying whatever they have to, to reduce the probability of legal issues down the line.
Yes, of course they've sacked him for his expression of his views, because they are such that might make the company vulnerable to being sued. It's a fairly unremarkable business decision; it is patently not useful to have a senior HR guy shouting about "loathing Islam".
You are inferring that whoever fired him, disagrees with his views. That doesn't logically follow at all. If I were his employer I'd be firing him too, even if I also "loathed Islam".
I think DEI is a bit of a scourge tbh (and I say this as a mixed race female immigrant etc) and businesses should have more freedom to make business-friendly decisions about hiring and firing.
This is one of those times. This man is clearly unsuited to HR, bye bye