What does Winston mean when he says, “The proles are human beings. We are not human.” How does the age difference between Julia and Winston affect their beliefs?

These two questions at first glance seem disconnected but they are, in fact, related. They both speak to the theme of memory, a theme which is integral to the novel's exploration of what it is to be fully human. Memory, Orwell posits, is essential to preserving one's humanity.
Winston's job, which requires him to constantly drop information down a "memory hole" meant to extinguish the past by burning undesirable written records of it in a furnace, is the height of dehumanization. Additionally, Orwell notes the existence of memory holes at frequent intervals in all the hallways where Winston works. In this dystopia, Party members are encouraged to destroy memory.
However, as said above, memory is part of what makes us human. As Winston regains his humanity through his relationship with Julia—above all his ability to love and care for another human—he finds memories of his own past resurfacing in his dreams. He remembers more and more about his childhood: he grew up in poverty but lived in a relatively "normal" home. He was cared for by a loving mother willing to sacrifice her needs for his needs. He connects this to the life of the proles. He evolves from looking at the proles with the contempt the Party inculcates to understanding that they are the true humans in this society. They are not lesser or subhuman, and, in fact, they carry the future of humanity on their shoulders. This is because they live the ordinary life he remembers from his childhood, where people are bound to one another by ties of love. All of this, he realizes, has been killed in Party members. Even children spy on parents, and everyone lives in isolation—in fear of everyone else.
Winston's age difference from Julia gives him an advantage when it comes to memory. She adjusts to the society they live in as the only one she knows. He, however, can remember a time before the Party took over, and he can weigh his memories against Party propaganda to discern truth from lies. He knows, for example, that contrary to what the Party teaches, it did not invent the airplane. He also knows he is of the last generation that will have any memories of life before the Party. This helps him have a sense of self distinct from the Party—the ultimate thoughtcrime.

When Winston says that "the Proles are human beings," he means that they are not subject to the same restrictions as Party members. Specifically, they are not subjected to the constant, invasive monitoring of the telescreens or hidden microphones. They are not brainwashed by propaganda nor by the Party's constant rewriting of the past. Moreover, the Proles are free to marry whomever they choose, drink in pubs, and gamble. In other words, the Proles control and dictate their pace of life. For Winston, this means that they have retained some measure of humanity which no longer exists in Party members.
The age difference between Winston and Julia plays a significant role in their beliefs. Because he is much older than Julia, Winston can remember what life was like before the Party came to power. In contrast, Julia has only ever known life under Party rule. As a result, Winston's beliefs lead him to want to recapture the past, a past in which people, like his mother, were free to form their own loyalties with others. Notice that Julia does not understand or share this belief. Instead, she wants physical freedom and escape, as shown by her strong sense of sexuality.

Winston recognizes that the proles have certain freedoms that Party members do not have and can express themselves in certain ways that Party members cannot. Unlike Party members, proles are not constantly under surveillance and are not required to attend government functions. They are free to engage in relationships with the people they choose and do not live in constant fear of the government. In contrast, Party members live restricted lives under the constant watch of government agents. Party members are forced to appear and act completely orthodox or else risk being arrested and tortured in the Ministry of Love. They are not free to love whoever they choose and must suppress their negative feelings at all times. In this sense, Party members do not enjoy typical, free lives like the proles, which is why Winston does not consider Party members human beings.
In regards to how the age difference between Winston and Julia affects their beliefs, she is less concerned with undermining the political system of Oceania and more focused on having a good time disobeying the strict rules of society. Winston is more concerned with understanding and challenging the entire government of Oceania. While Julia enjoys having an affair to fulfill her suppressed sexual desires, Winston views their first sexual encounter as a political act.