How do you know if an act is a sin if you dont belong to that religion?

I think ShadowWalker made an accurate assessment above. I'm an atheist and would simply say what she asked you to do was wrong (as opposed to a sin). In general atheists treat others the way they'd want to be treated themselves, but occasionally you'll find one with questionable morals, just as occasionally you'll find a religious person who engages in amoral behavior. I believe that morality is innate. Humans have a variety of tendencies that help them fit into society, including the capacity to feel empathy and act altruistically, a sense of fairness, a desire to be respected by others and an ability to feel shame (that occurs even when no one is around to witness a misdeed). I suspect people experience these tendancies to differing degrees, so that some end up more morally upstanding than others. Family upbringing and cultural background also likely play a role in our moral development. People can be taught to ignore empathic tendencies in some circumstances (for example, killing being permissible in war, or, sadly, it being acceptable to ignore homeless people asking for help). I believe the Bible and other religious texts summed up what was considered morally right among the population at the times they were written. In modern times, you can find written codes of conduct in work places, schools, and other institutions that are more directly applicable to encouraging groups of people to get along with each other. The authors of such codes, are simply spelling out what the average person already knows. Maybe they hope their directives will incite a jab of conscience in those whose moral standards are a bit lax, but the majority of people would probably have lived by those guidlines without ever having to have seen them written out. So, in a sense, atheists carry their book of rules on how to behave around with them in their heads. Since I have young children, I also happen to have a number of books in my home that teach values like honesty, responsibility, sharing etc., but they just reinforce what my kids are already learning from observing the adults around them, and from interacting with other children. (e.g. if you don't share, people don't want to play with you). At any rate, I hope your experience with atheists hasn't been limited to your encouter with that woman. It's not typical of how most of us behave.

Not all atheist are like the lady you came across. Even though they don't believe in God most atheist believe in the samethings we do. Not to steal, kill, commit adultery, etc. To me adultery is a sin too so I think your response was the correct one.

To know what is a sin or not, you have to listen to your own conscious because that tells everytime you do something wrong or a sin.

Just because she's an atheist does not mean that morally she should respect the fact that you're married and d'ont want to cheat on your wife. I think that if she wants to sin might as well she sins with another atheist.