At the bare minimum, racial and gender equality.
Where does that exist in 2016? I live in the soi-disant most feminist country in the world, where somehow they've never had a female prime minister, and there's still a noticeable gender gap (women make 93 kronor for every 100 men make in the same industry as of ten years ago).
I assume what is meant are Western social attitudes (which are far from universal even in the West of course. Compare American and Canadian attitudes towards the death penalty.) So:
- Sexual equality
- Gender equality
- Racial equality
- Secularism
- Enviromentalism
- Universal sufferage
Anything else?
Um, okay. So let's unpack this:
1. Sexual and gender equality: lol. If you want to contrast the kind of sexual division of labor that's common in developed countries today with what went on before the 1960s (in 1950, the US had the same pay gap as the UAE and Qatar today, taking into account women's low workforce participation rates), or with premodern attitudes, then fine. But in some ways, attitudes today would be recognizable to premodern urban workers: in medieval and Early Modern Europe, it was expected that women would work, but that men would be the primary earners. The sexual division of labor grew more rigid in the Industrial Revolution, and then transformed into what we all know today as the traditional postwar mentality in the Second Industrial Revolution. This came out of the discovery of the germ theory of disease, which led to public campaigns for cleanliness, which put the onus on women to make sure their homes were clean and healthy. In that sense, 1860 was more modern than 1950.
1b. Marriage ages in Western countries today are within the same range of the Early Modern era, for both genders. Today, people delay having children until they have enough financial stability to afford them, which usually means late 20s or early 30s. This was the same in Early Modern Europe for people who were not aristocrats; the difference is that today, people in developed countries stop at 2, whereas in 17c Europe they averaged 6. Marriage ages went down in the Industrial Revolution again, and bottomed in the postwar era, because of issues involving drag from the Depression.
2. The problem with talking about racial equality is that it raises the question of what race is in the first place. In the entire first world, both in the West and in East Asia, race is deemed to be a combination of genetic origin, and skin color and presence or absence of epicanthic fold; but until recently, language was as important, and still remains a significant ethnic marker in Europe and a barometer of assimilation among immigrants. In 1500, this was more or less the case in China, with its division of the world into Chinese and barbarians, but in Europe the primary marker was religion; it was only in the 16c and early 17c that Europeans definitively stopped viewing conversos as Christians and releasing black slaves who converted to Christianity.
Of note, there was substantial black slavery in Lisbon and Seville in the 16c - in 1500, Lisbon was about 10% black - but manumission rates were high since slaves were not needed on farms, and instead of forming a discrete ethnic group as in post-abolition America, many blacks rapidly assimilated. If you follow social justice Tumblr and Twitter accounts, occasionally you'll see a reference to a famous European's having substantial black ancestry - for examples, Pushkin was one-eighth black.
Oh, and to complicate matters, the growing visibility of Muslims as the West's them-group is slowly restoring the role of religion as a primary marker of otherness.
3. Secularism: yes, this is a major shift. In the Europe of 1500, atheism was a kill-on-sight offense. That said, in 1860, the role of religion in urban Britain and France wasn't much greater than it is in the US today; in France, it even was a partisan issue along similar lines to those of the US today. Rural areas stayed religious for much longer, but there are enough parts of the US Bible Belt where people won't talk to you if you don't go to church that I don't think there's been a huge sea shift.
4. Environmentalism: that's kind of dicey, because I could probe and ask what this exactly means. If it's about regulations on air and water quality, then these existed earlier than people think. Early 19c Britain had a rule requiring railway locomotives to consume their own smoke, which in effect required them to burn coke rather than coal until mid-19c improvements in steam engine technology reduced the amount of pollution produced by coal. American cities had rules banning the operation of steam-powered railroads, so railroads had to change from steam power to horse power for the last few km.
The big changes, all of which have happened since the late 19c, are attitudes toward wilderness and the third world (and marginalized groups in general). In brief, there was a shift from viewing wilderness as a horrible thing to be tamed to viewing it as a treasure to be safeguarded, including from the people already living on it. This happened in the US Gilded Age and Progressive Era, and moving it to the other side of 1860 with a 1500 POD is just a matter of having the Industrial Revolution happen a bit earlier.
Later, around the 1960s, movement environmentalism shifted toward listening more to people living in the affected areas, which was partly about civil rights and decolonization, and (in the US) partly about the failure of the Smokey Bear mentality. The Smokey Bear failure happened when it did because of technological improvements making it possible to turn off forest fires after WW2. Moving that to the other side of 1860 is harder - it requires speeding up tech progress by a century, which probably could be done with a 1500 POD, but would be as contrived as Decades of Darkness (and that's praise by faint damn).
5. There was universal male suffrage in Switzerland in 1848, as well as in France before Napoleon III's coup. Advancing women's suffrage a couple decades is plausible, even if you do not play with tech levels too much.