Hey, OP, I actually have a really similar problem, so I totally get where you're coming from. My husband isn't rude with staff but he does completely shut down, get impatient with me and bury his head in the sand and generally just totally minimise things when I'm sick.
He's otherwise the world's most amazing husband, it's just that when I'm ill he behaves like a complete penis every time. It's like someone flicks a switch. He becomes stressed and impatient and minimises everything, as though I'm somehow making it up or overreacting. I had a very traumatic labour and life threatening complications afterwards so it's not as if it's situations where I'm making a fuss over trivial stuff.
With emotional stuff he's usually great, he was my absolute rock when my dad died, for example. But he just loses his shit over anything medical.
I think this kind of thing is probably quite common. It's probably a combination of fear, feeling helpless and denial. It's almost emotionally easier for him to pretend it's not that bad and I'm "overreacting" than to face up to the seriousness of the situation. Basically, it's him handling a specific type of stress very badly.
All that being said, it's not acceptable behaviour.
It's also a really difficult thing to deal with in the heat of the moment. Last time my husband pulled this shit, I outright told him to fuck off and sent him home. We had a long talk after the fact about how he behaves when hospitals and medical stuff are involved and he was in total denial about his behaviour but eventually accepted that it might be an issue. I'm not optimistic that he won't just shut down again next time, though and if we're lucky enough to have another child I'll honestly be thinking twice about having him there at the birth.
Sorry OP, I know this isn't really a solution, I just wanted to let you know you're not alone and also that it's perfectly possible for someone to be otherwise great and then just be a complete moron in one specific scenario. Is he otherwise a good partner?