I'm one of those people that comparative strangers randomly confide in. The flip side of having an approachable face is that angry loons often choose me to rant at. Friends have expressed amazement that it really doesn't bother me - it doesn't, I'm even quite interested sometimes!
I've always known that ranters, ragers, wailers (and screamers at the Sistine Chapel) are doing their own thing. If there's a nugget of truth in their histrionics, it could be worth later consideration but the emotion explosion is all about them. In fact, it's often literally about them: their accusations are quite likely to be self-criticisms misdirected outwards.
I couldn’t care what my neighbours think of me but I do say for instance what my family think.
Same. If you think your family member's right to criticise you, take it on board and be gracious about it. If you disagree with them, that's all there is to it - you disagree. They have a right to express their opinions; you have a right to feel differently.
I haven't read "Let Them" but was very pleased when it came out - I hadn't realised so many people were so distressed by other people's thoughts & feelings. It's great that there are now books and podcasts, etc, giving everyone permission not to care about stuff they don't need to care about!