How do I stop accidentally offending people from other cultures?

First, breathe. If you were the kind of person who did not care, you would not be asking this. Meaning no harm and still causing it is not cruelty; it is inexperience. That can be learned out of. Most offense comes from assuming your normal is everyone's normal. So slow down and get curious instead of confident. Watch how people respond, ask when you are unsure, and when someone signals you crossed a line, treat it as information, not an attack. A simple, sincere sorry, tell me how you'd prefer, repairs far more than perfect knowledge ever could. Here is your step: the next time you sense you misstepped, resist the urge to explain or defend yourself. Just apologize plainly and ask. People forgive the honest learner much faster than you think. It is defensiveness, not mistakes, that does the real damage.