That decision would have been up to HR and the executive team. I was neither.
Speaking personally, if the company hired an interpreter, I would have been OK with it. If the company insisted on having all design meetings in a chat room, I would think that crazy. Most people's typing speed is a small fraction of their speaking speed.
Actually that decision would not have been up to HR and the executive team, would it? In the United States, that decision was made for you at least 28 years ago, right?
You're referring to the Americans with Disability Act. What it requires depends on the "essential duties of the job" and what is consider a "reasonable accommodation". Those are judgement calls. Those judgement calls need to be made by executives on the advice of HR.
My lay understanding is that the law does not insist that the job requirements change. So if being able to participate in design meetings, daily scrum, and so on are daily requirements for anyone to have a programming job at your organization, they are essential duties. Even if the same job title in another organization has different requirements. (But can you document your requirements?)
That brings us to the question of what a reasonable accommodation might be. Hiring a full time interpreter to follow that person around is probably considered unreasonable. Allowing someone who lip reads a device that can do text to speech is clearly reasonable.
The ADA affects the decision. But it doesn't make it for you.
This is a really weird argument. It seems unlikely that you would succeed in legally justifying excluding deaf people from your team based on the idea that verbal communication is an essential duty of a software developer, which is the analysis that would likely be used against you.
Also: if your management decided to exclude deaf people from your team, wouldn't you quit? I would quit.
The judgement call of whether to act on an argument like that is not up to you and me, it is up to HR and the executive team. If it comes to court, the validity of the argument is up to a judge.
As for protesting choices that you don't like by quitting, that is your right. Speaking personally, deciding not to hire someone because you believe that they will be unproductive in that role seems to me to be a perfectly reasonable thing for a business to do. And I don't see a moral distinction between different reasons why someone is expected to be unproductive.
Speaking personally, if the company hired an interpreter, I would have been OK with it. If the company insisted on having all design meetings in a chat room, I would think that crazy. Most people's typing speed is a small fraction of their speaking speed.