I am not sure if I agree. I'm a cancer survivor and when I was going through surgery and chemo it actually did help me to have friends drop a line saying "Is there anything you need?"
I reached out to my black friends with something similar, variations on: "Thinking of you. Let me know if you want to talk or pray." And they all reacted positively.
Of course, I think the key is that they are my FRIENDS, not acquaintances. One of them has known me for 31 years. He and I have done road trips together, we've stayed at each others' homes and met each others' families. So these are intimate relationships, and I know that this type of response will be OK with them.
I think really it comes down to relationships and treating people as individuals. If you don't know someone well then it's presumptuous to insert yourself into their life, particularly if you're doing it mostly as a form of "virtue signaling". If you're actually their friend you'll be there for them. If you're just an acquaintance, it can be disrespectful. JMHO