So, from my experience, I really cannot say that there is any kind of extreme attitude towards renunciation and secular families, and one may want to get a broader picture before coming to conclusions.
This is fair as you have much more exposure and experience with Chinese culture and monasticism than I do. And certainly the way FGS and other institutions take care of the older monastics and the poorer families of those monastics is exceptional (I fully realize with my decision to work within Tibetan Buddhism I could be out on the street in my old age- this is something I worry about from time to time- I am only human! But what can I do, this is the tradition where I function the best and connect better with the masters)
But in the clip Master Shen Yen did say for many parents the renunciation of their children was worse than if the child had died. (Definitely I don't think he was encouraging this attitude, but the fact he mentioned it and Fa Gu San included it is a video indicates to me that enough people think this way for the master to want to respond to it).
There are of course devoted temple families who might even encourage their children to ordain and are disappointed when they become accountants/retail managers/lawyers/schoolteachers etc. instead of monks or nuns. I have met some, but not many. The initial period of seclusion that many of the seminaries insist on, not allowing letters or phone calls, seems to be difficult for many families (I am not sure how this varies from temple to temple).
But many of the Chinese monastics I have met and continue to meet told me that their parents were, at least initially, very upset with their decision to ordain. I have a friend whose parents told her she must wear a wig when she comes to visit as the embarassment of her ordination would shame the family. I have also heard several stories of parents appealing to the abbots several temples not to ordain their children. In one temple in Taiwan (not FGS or Dharma Drum, but another large one) when the master ordained some monks and nuns without the permission of their parents, the parents came to the temple and tried to take them home.
Even the parents of Western monastics I have met over the years do not tend to have such a reaction (though some are initially upset). And certainly it seems that in Tibetan, Thai and Viet Namese families the parents are overjoyed when their children enter the temple. This is changing somewhat in exile with the Tibetans (although not to the point of parents opposing the ordination of their children), but most of the families in Tibet think that if there is a monastic in the family it brings them merit (sometimes they even send children to the monastery that don't have a vocation for it, but that's a topic for another thread). Thai families are also very proud if a son can stay a monk for life, even in the rapidly modernizing country. Despite communism, many Viet Namese families seem to feel the same way.
If it is not a more conservative attitude towards renunciation that is the cause of this perhaps we could look at other cultural and insitutional factors,
I am not sure as to the sociological/cultural reasons for this difference. Initially I thought it had something to do with communism, but that is also a factor in Tibet and Viet Nam, as well as several of the Theravada countries. If I could venture a guess I would say that maybe it has something to do with the strong Confucian values that still permeate Chinese culture. Buddhism seems to have been a difficult fit, as when it entered China there was already a strongly established culture and social framework. To me it seems that in many ways Buddhism and Confucianism are diametrically opposed, though certainly many great scholars have tried to reconcile them.
So to me it seems their is a clear difference. I am not setting the blame for this only with the temples at all. But there does seem to be something within Chinese culture that sees it as a pity when a younger person ordains. And certainly parents often seem to have a very strong influence over the career/vocation choices of their children, so my feeling is that Chinese Buddhism is hindered by this attitude.
That being said, in modernizing countries throughout the world the number of people wishing to enter monastic life will continue to dwindle for reasons other than parental opposition, but this does seem to be an issue in the Chinese diaspora.
In Western countries too, now, the number of people wishing to ordain is already markedly less than it was in the 1990s, at least in Theravada and Tibetan Buddhism. But I think this is due to the growth of "lay Buddhism"- a topic for another thread.