I don’t think Americans unanimously respect titles of nobility, and I think Gruber’s point is that he personally doesn’t respect them and wishes Apple didn’t respect them either.
Whether this is a consistent point of his, whether Gruber has always referred to the Queen as Elizabeth Windsor, I don’t know. But I wouldn’t conflate convenience with respect. “The Queen” is a very easy name to remember and use informally without necessarily supporting monarchy. Like, I wouldn’t call Captain Blackbeard “Captain Blackbeard” out of respect for piracy.