I've written about this before!
The Cultural Revolution was absolutely devastating for Confucianism and filial piety, along with a great many other institutions of Chinese culture and history, such as Buddhism, regional customs, and Chinese folk religion.
The very nature of Chinese society was radically changed and its effects are still being felt strongly today.
The famous purges of intellectuals, urban dwellers and individuals labeled capitalists, bourgeois or political enemies (and their families), closing of schools, burning of books, and defacing of temples were only the tip of the iceberg.
The Cultural Revolution itself seems almost impossibly complex, nevermind the far reaching effects.
It is a long long story so I will break it down very generally here. If you want to learn more about it Born Red: A Chronicle of the Cultural Revolution by Gao Yuan or Mao's Last Revolution, by Roderick MacFarquhar and Michael Schoenhals, are both great starting reads to introduce yourself to the topic.
The goals of the Cultural Revolution were solidify communism as the one authority, reeducation of city people, and distract the common people from the failure of the Great Leap Forward.
As with any revolution, until they completely legitimized their rule, there is always a perceived danger of counter-revolutionary elements. Communist ideology often warns of the need for vigilance against this. This paranoia helped them cement their power and hold over the nation. Unfortunately, it meant that anyone even suspected of being not Communist enough was publicly humiliated and mentally, sometimes physically, crushed underfoot by wrathful crowds.
There were quotas of "subversive elements" that had to be found per community by any means necessary. Meaning innocent people would be declared enemies of the people at random. At worst, Party officials and members could use this to act out grudges.
To imagine what this is like, imagine where you live. Everyone you know for miles around would come. They declare your parents to be evil anti-Communists, enemies of the revolution and the people. You, your friends, your parents' coworkers, your doctor, the kids down the street, everyone begins to verbally abuse them with a hatred that is palpable.
Why? Because it is required.
If you don't there could any number of Party informers mixed into the crowd carefully gauging whether you show enough emotion, enough rage for the Party. It could be your old teacher. It could be your boss. It could be your auntie. It could be the dog next door. You can trust no one.
The repercussions were massive. The previously open and community focused Chinese people became introverted and closed. When asking a Chinese person where they are from, they will not say "China" or "Taiwan" or the PRC. They will say what village they are from, and they proudly speak with others from their region in their own dialect, often unintelligible to outsiders.
There is a strong sense of belonging to local communities that is deeply tied to Chinese culture dating back thousands of years. The Cultural Revolution destroyed this.
To directly answer your question, filial piety roughly roused from its bed, shot twice in the back of the head and then had its body was paraded through town. Filial piety was not deemed relevant in the new order that the Party was trying to bring about so it, like many other undesirable elements of society, culture and history of the time, was forcibly removed. And the CCP was very open about their efforts in doing so, celebrating even.
Of course, the process wasn't as simple as 'you may no longer practice filial piety'. It was much more insidious than that. There's something to say for the efficiency and effectiveness of the CCP's propaganda workers as well as political agents that would instigate public denouncements, political inquisitions, and plant suggestions, driving wedges between people.
All the bonds that Confucianism valued, teacher - student, emperor - people, father - son, husband - wife, etc. were worth very little in the ideology that Mao wanted to drive home into the collective minds of the Chinese people. So they moved to weaken the traditional institutions.
Schools were closed and intellectuals were demonized. The unemployed and aimless students are recruited en masse into youth groups or Red Guard units. They're encouraged to root out enemies of the party and given free reign to accuse ex-authority figures like their teachers and parents. Parents and teachers in turn begin to worry and doubt their children, afraid they might be the next to have activist children 'rising up'. Spouses, friends, and neighbors aren't exempt from this pervasive doubt. Traditional family and community bonds are weakened or broken.
Then, many youths are shuffled about in the great project to re-educate the masses in the joys and virtues of communist agricultural society. This separates them from and further alienates children from their parents and schools while allowing for them to be closely monitored as they are taught new lessons about ideology, the virtues of the party, and the values of their new lives.
The party is their family now, the senior cadre members their teachers, and Mao is their Emperor.
Some wonder why many Chinese people have learned to look out for themselves and their closest circle of friends and family first and foremost, seemingly callous and completely unsympathetic to the plight of their fellow humans. You chalk some of that up to the Cultural Revolution. It destroyed entire generations' sense of community, belonging and trust. Brothers doubted brothers. Parents were afraid of their children. Every neighbor watched one another.
We haven't even really gotten to the moving of people to the countryside yet (most of the urban dwellers moved were kids still in school and totally unprepared for a life on farms, in factories, and the rural life), closing of schools for 5 years and longer in some places, crushing of local markets, and the deliberate organized destruction of historical sites, temples, artifacts, and book burnings. We haven't gotten to the Cult of Mao yet nor the invasive propaganda of the period and haven't even begin to look on the political side of things. We also haven't looked at the rich folk religion culture and traditional art that was swept aside and supplanted by propaganda.
The Cultural Revolution was such a massive disaster that Chinese people are still figuring out how badly it messed up the collective psyche.
The famines might have killed tens of millions but the Cultural Revolution might have killed a billion souls worth of culture, creativity, and community.
Sorry for the rambling and I hope this answers your question. Feel free to ask follow up for clarification! Cheers!