Here is how this goes:
Person 1 says statement x.
Person 2 is offended by statement x.
Person 1 says "I don't mean to be offensive."
Person 2 says "I was offended because statement x means y."
Person 1 says ' I didn't intend statement x to imply y.' or else 'statement x doesn't imply y.' or else 'there is nothing wrong with y.'
In other words person 1 doesn't think their comment is offensive and person 2 does think it is offensive. What do?
if you accidentally rear end the car in front of you, it doesn't matter if you didn't mean to. Now saying offensive things is obviously different from crashing into someone, but the principle is the same: your intention doesn't count for shit. THe caveat is that if you do say something offensive, and everyone says things that some other person would find offensive, you aren't a terrible person. So the conversation should go like this:
Person 1 says statement w.
Person 2 is offended by w.
Person 2 says "I am offended by w for the following reasons x,y,z."
Person 1 says, "Ah, I see why you find that offensive, however I did not mean to be offensive,
I will speak more carefully in the future to avoid these situations."
Person 2 says, "Even though I was offended, I recognize that you did not mean to be offensive, you are not a terrible person but what you said is offensive."
And then everyone can move on with their lives after acknowledging the subjective nature of everything.
Note: This only applies to circumstances where Person 1 (the offender) actually does not hold prejudice, racist, sexist, classist beliefs, and merely spoke uncarefully. If someone is a bigot by all means feel free to call them out on their bigotry. (Deck Knight would not get a pass).
edit: also scientific racialization is in a constant state of being debunked. It is 'just' a social construct (social constructs are real af, but race is often talked about in a way that could lead someone to believe there is something physical about race) and everyone (the academic consensus) admits it except for doctors. biologists admit it, geneticists admit it, only the medical profession still holds out because they think they are obligated to take 'race' into account when making diagnoses:
https://en.wikipedia.org/wiki/Race_and_health#Controversy_regarding_race_in_biomedicine