I realize this is now drifting slightly off topic, but I was brought up that you should apologize when you have done something that you did wrongly and do not intend to repeat. If I step on your foot, whether by accident or intention, I should not have done so, and I do not intend to do so in the future, so it would be appropriate for me to apologize. If I say or do something which is not wrong but which upsets you anyway - telling you I think Worm sucks, say - even if that makes you upset or unhappy, I would not apologize for doing so.If you unintentionally upset someone else, I think apologising for it isn't a step to support their worldview, it's a more basic polite acknowledgement of 'I made a mistake'. A more deep expression of sympathy and support might be likened to bringing someone soup and orange juice, but a quick 'Sorry, my bad' is more like... well, I keep bringing the conversation back to stepping on someone's foot because that was an analogy I once saw used by someone much more eloquent than me to explain such things, but I also think it's a good analogy; sometimes you step on someone's foot, and then you go 'oh, sorry about that'. I don't think that falls under 'kindness' as you're defining it?
And indeed, to go back to kindness, apologizing for something which you do not think is wrong because it upsets someone is precisely kindness in this typology - it is supporting their worldview as to what is wrong, I would say?