I am going to put my authority forward on this as DM and state:

You can play whoever and whatever you want, it is a fantasyroleplaying story for a reason.
 
I will not tolerate people who feel the need to tell someone they can or can't do something 'because they might feel offended' or 'feel the need to feel offended for someone else's sake' type of nonsense when there is no foundation for it.
I consider this time of behaviour bullying.

It is a character. Your character.

Unless you are going completely over the lines with this and be a complete jerk for the sake of being a jerk and demeaning I say hardly anyone truly could have objections to it.
  
I will say straight up I don't like people who feel the need to lecture others. The world is tough enough on people as it is, no need to add more to that. Maybe its because I am a bit older and this whole current wave of SJW-ism is making my head hurt and 'my bullshit detector' go off.

But writing someone who is deaf as mentioned before by [@Dark Cloud] can be a bit difficult, but challenging as well. If you want to do it, be my guest.