This is a weird question, because it's extremely difficult to compare cultures with a huge generational gap, as people live linerally and react/are influenced by things in sequence.
In a sense, then, there were no real Victorians alive when the cultural revolutions in the 60s started. Sure, perhaps some curmudgeony old man scorned or was generally terrified of all the social change and upheaval happening, but that's kinda getting away from your point, I think. Please keep in mind that Victorianism was wholly and entirely dead after two world wars, the Great Depression, etc. For example, try asking your Gramma about social issues, etc. Mine was born in 1921, but hers is an opinion influenced by all the eras she's lived through. A "true" Victorian would have to have been born somewhere in the 1830s or so to really get at the social and cultural understanding of the era.
So let's consider what lies between the "postmodern" and the "Victorian", to use very over-arching terms. It's the modern, of course. The era of social change and literature/art that responds to the sentiments of the Victorians while trying to understand their place in the world following the first World War. This era was categorized by a huge shift and rethinking of things generally taken for granted, the advent of psychology, a huge amount of sexual and societal freedom (comparatively), and more.... cognitive attention given to a decentralized world view (for Europeans, at least, American authors practised this but I can't speak for the politics or the people).
Victorianism is defined (loosely), with the following "cultural" touchstones:
Sentimentality
Propriety
Optimism
Progress
Social Roles
Race Realism
Moral Obligation <--- This was the huge one, people really felt obligated to 'help' others live a better life. Preying on the social idea of sentimentality, so much of the literature and art of this period preys and plucks at people's emotions in order to help them enact social change (Dickens especially does this through his depictions of children and factories). With no governmental oversight of works and people, people felt that it fell to them to move society continually in a foreword direction.
See, we think of the Victorians in extremely repressed terms, and perhaps compared to our modern sensibilities they were, and perhaps even compared to the late 17th Century, they were, but the real damning aspect of the Victorian lifestyle wasn't necessarily the 'sexual repression' but the splitting of the roles (separate spheres) ideology that pervaded fairly in-tact to the 60s despite being challenged in the modernist era.
Yes, women could be 'fallen women' who were ostracized for having extra-marital affairs, and yes, divorce (for women) was extremely difficult and lead to them being trapped in hateful marriages, but this was more from the fact that men and women were supposed to lead completely separate lives that were only tangentially related. Women were domicile hometakers that made the "domestic sphere" a safe haven for their husbands, who had to face the 'ugly and awful' truths of the 'real world', and thus be calloused and hardened by them. So quite like the 'mouse house' craze of the 60s (challenged so beautifully by Pynchon in The Crying of Lot 49) was quite connected to this idea, and Victorians would understand this as a positive thing.
As for sexual repression, Victorians hardly blushed at an exposed table leg. Rather, the new middle class needed to differentiate itself from the working poor, where women had to work in factories and be part of general society. So, if you had the money, you would dress in fancy (stuffy) clothes, get your wife to stop working, and not deign to address the crude and vulgar things that interested the poor (sex, etc). The frankly insane amounts of effort put into this social separation was strange-- after all, social mixing was quite common in the 18th Century in community gardens like Vauxhal. But now, the difference between being middle class and working poor was a razor thin margin, and with how rapidly technology was displacing people, the new middle class really wanted people to know they were not part of the working poor. This sort of social differentiation is quite common in our society as well, think about the things that people do or say if they rise above a certain social echelon.
Anyway, now that we have a sort of idea of Victorianism, let's look at what modernism changed. In effect, it really started to break down that fastidious moral absolutism and sentimentality that the Victorians believed in so strongly. With the advent of 'modern' psychology (Freud, Yung), concepts like the subconscious 'exposed' the hidden evil within us all (so to speak), and the idea of 'purity (in public)' was extremely heavily challenged.
For example, consider Tom Hardy's novels. Often seen as a bridge between the modern and the Victorian, his novels are strongly rooted in Victorian values and concepts, but he challenges many of these to show how society is changing or flawed. Tess is a great example, where a young woman is raped, becomes pregnant, and is later forced to cohabitate and serve her rapist. Where earlier novelists (Dickens in Bleak House) may challenge this trope by playing on people's emotions and sentiment through showing how awful that situation is for the woman and how it eventually leads to her death (because 'fallen women' were dead already, c'mon), Hardy goes the opposite way and gives Tess *gasp* agency. She (very eventually) kills her rapist, and even though she is captured and killed, this is shown to be a terrible act rather than a long-expected ending.
So by the time Mr. Ernie Hemingway steps up to the plate (along with DH Lawrence, Virginia Woolf, EM Forester, etc), the social landscape is already much more open about social mingling and sex. Consider how innately sexually charged Fitzgerald's Great Gatsby is. The Sun Also Rises (Hemingway) is blatantly about (male) impotence and sexuality.
So the changes leading to Postmodernism came slowly. By the time we get to the sort of irreverence that Pynchon and Vonnegut capture, you have fifty or more years of people challenging these deeply entrenched Victorian values and trying to replace them with something. Of course, the Hippies and the postmodernists did not really have good answers for how to replace these values, and so many people returned or reinforced their idea of a 'proper' family structure (nuclear family, wife at home, suburban life, no cross-class mixing). For examples of the sort of regression we're dealing with here, compare Nella Larsen's books Quicksand and Passing (that captured the Harlem renaissance) with Toni Morisson's debut The Bluest Eye. I'll tell you right now, Morisson's book betrays a much more inherently distressing picture of American race relations and internalized racism than Larsen's book does, despite them both being overtly about race, racism and understanding.
SO FINALLY, TL;DR:
Open sexuality was less troubling to the Victorians than you might think, and if you want to see how they would react to the cultural shifts occurring in the 60s, look no further than 'typical family values' exhibited in suburban america.
Consider how certain critics respond to 'postmodern' books and the 'values' they capture. Vonnegut and Pynchon were reviled by certain contemporaries because they did not capture 'proper' domestic values. Jameson, a famous Marxist, famously called postmodernism "Blank parody" with no substance or contributive aspect.
Arthur Miller's Death of a Salesman is a good place to start.
(I specialised in literature, as you can probably tell, but lit is a really good lens into culture and cultural values, so that's the approach I chose to take. I am also traveling at present and so it is a little hard to provide sourcing. If you would like, I can provide some resources for you later).