Religion is a piece of everyone's social identity, every bit as much as gender, ethnic, and national identity. Often, religion is correlated with ethnic and/or national identity, if not one and the same. If you are Jewish or Hindu, your religion and ethnic identity are inextricably intertwined. If you are Native American, Maori, or Australian Aborigine, chances are that you have a religion completely intertwined with your tribal identity. Even those who have become Christian, or whose families have, more often than not intertwine Christianity with traditional religion.
Even religions that originated based on ideas and teachings meant for everyone, rather than tied to ethnic identity - Christianity, Islam, and Buddhism being the best known examples - are tied to ethnic identity in the minds of many, and often in practice. Unless they or their parents or grandparents converted to something else, or are a religious minority where they came from, people of European, African-American, and Latin American descent are typically Christian; people of Middle Eastern but not Israeli descent are typically Muslim; and people of eastern Asian descent are typically Buddhist (which may be combined with other religions such as Shinto or Taoism). They may be anything from very religious to just nominal members of their faiths, but this particular religion is likely to be a piece of their identity, or to have been at some time in their lives.
And within those faiths, who belongs to which particular branch of the religion tends to correlate with national, ethnic, and regional identity. Tibetans practice a different form of Buddhism from Cambodians or Laotians, who practice a different form from the Japanese. American Protestants stand a greater chance of being Southern Baptist if they're from the South, and a greater chance of being Lutheran if they're from the northern Midwest. Most Iranians are Shi'a Muslims; most Saudi Arabians are Sunni. An Italian who is not Catholic and a Greek who is not Greek Orthodox would be the exception to the rule in their respective countries.
Any religious conflict, anywhere, that reaches the level of violence is based more on ethnicity than on religious belief. The strife between Protestants and Catholics in Northern Ireland is really ethnic rather than religious. The Protestant English invaded the Catholic Irish, and their respective descendants mostly belong to the faiths of their ancestors. So it's not so much about Catholic versus Protestant as it is the Irish versus the English, natives versus invaders. The Islamic world has a similar, and ongoing, history of conflict between Sunnis and Shi'ites, which is even more tied to ethnic and national identity than Catholicism or Protestantism in the Christian world.
Of course, not all religious differences involve trouble, let alone bloodshed. In many places, it's the norm for people of different religious backgrounds to live side by side in peaceful coexistence, work together, attend school together, and become friends. If one person in a group is Jewish, another Catholic, and another Buddhist, that may be irrelevant to their friends-except perhaps if the conversation turns to religion or to who celebrates which holidays. If someone whose religion mandates dietary restrictions is invited to dinner by someone of a different faith, explanations and accommodations may be in order.
This brings us to the next crucial point about religious identity: religion often mandates how we socialize. While no religion flat out tells its adherents what to say to whom when, most religions do influence social behavior, in ways ranging from the subtle to the obvious. Someone who wears a very obvious piece of clothing for religious reasons - a headscarf, a turban, a yarmulke, Amish dress - is automatically going to be regarded, and treated, differently from someone who dresses just like everyone else. In communities where everyone follows the same religion and dresses accordingly, someone who doesn't adhere to the dress code will stand out.
Likewise, if a religion mandates abstinence from certain foods or behaviors, it will influence social life. If you follow a kosher, halal, or vegetarian diet, where, when, and with whom you can eat will be influenced. If your religion forbids alcohol or dancing, or requires you to spend Sundays in church, Mondays with your family, or Friday evenings in prayer, that restricts your social activities in turn. And within those restrictions, you may find social opportunities not available to people who don't follow them. Praying with others and spending time with your family are certainly social activities.
More religions than not have something to say about how the sexes are supposed to act and relate to each other. Most call for chastity until marriage and sexual faithfulness within marriage. Many prescribe roles for men and women, some more strictly than others. Some religions mandate how each sex is supposed to dress. Who is allowed to lead worship and take other leadership roles often depends on gender.
Even for people who are only nominally religious, or adhere to no religion at all, religion has some influence on their personal social lives. The belief that decisions of what to eat, how to dress, when, how, and with whom to be intimate, are matters of personal choice (which is inherent in some religions, and always held by people who follow no religion) influences behavior every bit as much as religious restrictions do. And for everyone, religion is part of the culture. In America, Sundays are typically expected to be a day off, and more businesses are closed then, or have shorter hours, than any other day of the week. Christmas is a national holiday because so many people celebrate it. For many, Sunday and Christmas are not necessarily holy days, but they are still holidays.
Further still, if you are not religious, that too is part of your identity. Someone who says, "I'm not religious, I'm spiritual," is identifying him or herself, and claiming a social identity. So is someone who says, "I'm an atheist," or, "I have no religion."
Finally, religiosity, or lack thereof, always determines who you will date and/or marry. People who strongly adhere to a particular religious faith are unlikely to be comfortable with a partner who does not belong to their faith, or who does but is much less religious than themselves. People who are only somewhat religious or not religious at all are likely to choose partners with the same level of religiosity as themselves. Non religious people may be willing to marry outside the faiths they came from, and quite a few do - but even in those interfaith marriages, the partners share the same lack of religion. If, sometime after they've been married, one spouse decides to return to their former religion, or to take up a new one, there's a good chance of conflict in the marriage. This is especially likely if the other one remains non religious and/or does not wish to convert. And for people who are not necessarily attracted to the opposite sex, willingness to enter a same sex relationship depends on not being religious, belonging to a faith where that is accepted, or being willing to ignore that part of their religion's teachings.
Indeed, it would be very difficult to find an area of social life that is not at all influenced by religion, whether or not the individuals involved are religious themselves.