How they handle it will impact their credibility more than anything. Honestly a company that gets popped and responds with urgency, gravity, transparency and integrity might even come out ahead.
It depends on how it happened, too. If it was a nation state deal and no more details come forth, I vote no. If this is a finphisher type hack and they get humiliated and db/source dumped, then yes.
I've been out of the security game for years now, but I would say no. A security company is still a company. And companies are vulnerable to security threats from nation states.
It probably depends whether (and how) they confirm it was a nation state, though.
Probably. But it depends greatly on what happened and how they handle it.
Not necessarily. Realistically, you can't stop a nation state attack if they want to get in. If it turns out that the breach was caused by default credentials being used on a public server, then it's a different story.
FireEye worked for Equifax before Equifax was breached. I'm not sure their reputation can be harmed much when they are still here after that shitshow.