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.
Also: if your management decided to exclude deaf people from your team, wouldn't you quit? I would quit.