I disagree with you.
Use "mute" as reference to deaf people is offensive, along with "dumb".
Also, my VR counselor told me that I was right thing about report to manager about offensive word against me, however he said many hearing employers are unaware about consider "dumb" and "mute" as offensive that use reference on deaf people. He spent a representative to my workplace to discuss about situation with offensive word, that was happened after worker quitted and my manager finally got it now.
I don't accept "hearing impaired" as well but they are not more offensive than "mute" and "dumb", so I informed to DMV representative about don't like term "hearing impaired" on my driver license and they made report to state.
I'm deaf person and heavily fluent in ASL, that it!