I haven't played a mute character before, but I've threaded with someone who has to great success. For one, when they first threaded with someone new, they'd go into detail about how their character was communicating: in this case, with a small device that allowed him to type and display text to his conversational partner. After that thread, the mute character's player would assume the other player understood what was going on and would not go into such detail about their character's use of the device or only mention it briefly. This avoided creating the impression that they were beating people over the head with the character's disability; after the first thread, it became more of a background element rather than the central focus of every tag.

In cases where their character either could not or did not wish to use this device, they would describe his body language, but also include a "translation" in their description. This sounds a bit unwieldy, but in practice, it came across pretty naturally. For example: "He tilts his head at her. What does she want?" (not a direct quote, but you get the idea). In this way, the player was allowing their thread partner(s) to decide how much their own character understood, not forcing them to guess along with their character.

Really, as long as you don't beat people over the head with it and don't let it become the center of every thread, I doubt people will mind!