treaclesoda re "And when I say 'is that a commonly held view' I don't mean 'your view is wrong'.
I know from your comments this is a genuine question so I will add my views.
I think lots of people in England or Britain have different view. I would go to a neighbours funeral, if I could. But I would not expect a neighbour to come to mine. My mum's funeral is soon. I would not expect her old neighbours to come to it In some ways I would prefer only family and close friends. But if an old neighbour came who really liked her, so be it. One of my mum's neighbours was her friend for about 50 years. They are coming, and I am pleased about that.
I can see it is very cultural, just as those who go to anybody's funeral may find it offensive that I may not go to a funeral of someone I hardly know from my community. Likewise, as someone bereaved I would be surprised and really quite uncertain to see a number of people at a close relatives funeral who I did not know at all. I don't find it particularly respectful, especially if they are only going because they would be thought of badly if they did not go.
treacle re "How do other people pay their respect and let the family know that they have heard about the death and they want to acknowledge it? Or is it just not mentioned?"
They send a nice card, share a pleasant memory in that card. It's very comforting. They may send flowers or make a donation to the charity that the family is collecting for, which is often related to how the perosn died (e.g. medical charity). If someone feels they really want to come, that is lovely and is genuinely imporant, but if they had no connected to the deceased it would be for me meaningless if they were simply coming because it was expected.
(I am English but have travelled the world and understand a variety of different cultures.)
Treacle re "clearly this must be a cultural thing because to loads of other posters it is very normal that the close family dictate who can attend."
I don't think it is normal to tell people not to attend, I think it happens. It is quite different when a family says, as this one has, no young children, it is not actually saying specific people cannot attend because they don't like them or whatever, they are saying they do not want young children present. I think you are right this is a cultural clash BUT the family are presumably from the same culture so that doesn't quite explain it.
I am confused why people assume the family would be sure to take the kids out if they made a fuss, how could one be sure they would do that when they don't respect the wish to not bring them along in the first place. Might they feel the children have every right to be there even if they are making a fuss?
I wonder if anyone has asked these kids if they wish to attend! Our son is coming to my mum's wake, he was given the choice, he is 5, he doesn't want to come to the funeral.