Replace apologetic disclaimers like "I don't mean to sound disrespectful" with "This probably could sound disrespectful." The shift from a direct command to a probabilistic frame makes listeners less defensive by giving them mental space to find reasons the statement isn't offensive.
Stop using disclaimers. Instead of, "I don't mean to sound disrespectful," what I want you to say is, "This probably could sound disrespectful." Use probably. And what people do is it gives them a chance, and when they hear you, they naturally, oddly enough, think the opposite. So if I were to say, "This is probably going to upset you," what do you naturally do? You think of reasons why that's not going to upset you versus me saying, "Don't be upset about this," and then you start to actually go, "Oh no, there should be reasons why I should be upset about this." So instead of, "I don't mean to sound rude," "This is probably gonna sound rude," "This is probably going to sound impolite," whenever you say that, the other person then looks for reasons as to why it is not the thing that you said.
