My sister Becki is a middle school teacher, and she is very good at what she does, partially because she doesn't put up with any games. Her students respect her; they learn from her; and many of them even really like her. If all of our teachers were like her the U.S. would have the best education system in the world.
When one of her students starts a sentence by saying, "I don't mean to offend you, but..." or "I'm not trying to be mean, but...", Becki's response is, "Then don't." She knows those phrases are nearly always followed by something offensive, and a "pre-apology" doesn't make it okay. I had one of those "I don't mean to..." type of conversations yesterday.
We bought a "new" used vehicle a few weeks ago and needed to sell my beloved Honda. I listed it on Craigslist yesterday morning, and we sold it for full price last night. (Nice!)
After listing it, I e-mailed a local chat group to ask advice, since it's the first time we've sold a car to a private party in this state. I got great tips about taking cash only, forms we'd need, etc.
And one person e-mailed me privately, apart from the group-wide discussion, with some advice on who I should sell the car to. After advising me not to sell to a dealer, she added, "Hate to be prejudice, but no foreigners."
If that had been a student talking to Becki, and the student had said, "Hate to be prejudiced, but--" the sentence would have stopped there, interrupted with a very good piece of teacherly advice.