This will vary by person... But for me at least, it's worse when someone changes what they were going to say to try and avoid a topic they know might be sensit

This will vary by person... But for me at least, it's worse when someone changes what they were going to say to try and avoid a topic they know might be sensitive to you, especially if it was in otherwise "innocent", organic conversation. For instance, changing a joke with a cancer punchline to something else, on the fly, because halfway into it you realize it's going to offend one of the people present. Who certainly has already heard it, and knows what's coming. Now, not only have you reminded the person of what you were trying to avoid, but you've also created this awkward tension where you-know that they-know, but have to pretend you don't know, because of the social "gesture" of changing their joke for you. Even if the fact that they're coddling you negates that gesture and then some. The more extreme example of this is the scenario where kids in school are sharing stories about, eg, their mom or dad, and when you get to the orphan, you either skip over them, or ask them a completely different question than everyone else, without acknowledging and explaining why.