Appreciating other cultures than those one has been exposed to naturally is difficult and time consuming, requiring a mixture of empathy and a willingness to learn. What one can gain is a deeper understanding of the human condition, and the more that one approaches immersion into another culture with zeal, the easier it becomes to connect with people from around the globe.
You need not necessarily accept every aspect of another culture, every society has its faults. Pluck the gems you come across as you are exposed to new ideas and practices, those things that you can incorporate into your own lifestyle. This process is highly enriching, and is how humans have advanced as a species through the ages.
It is no coincidence that when two countries that previously never had direct contact begin to exchange the elements of their respective cultures, that giant leaps in innovation regularly follow. I take this idea a step further though, and suggest that even in a modern internationally connected world, the separation of physical distance means that people will continue to differ regionally, and thus benefit in analogous ways when they meet travelers.
This expanse is far more easily traversed however, and those bold few that choose to explore outside the confines of the nation they are born to are afforded the same opportunities as any trade vessel in Victorian times. One may feel that they need not even physically travel, with resources like YouTube shared everywhere the latest top single of each country is a few web pages away.
Purchasing things like novels or traditional clothing online, watching television shows and generally experiencing a culture remotely is only scratching the surface though. Nothing can compete with getting out and being among people; shared experiences bring us closer together. Taking a superficial approach to learning about new cultures is a waste of time and effort, when one can spend that same time getting to know the people who live it.
All the little nuances of daily life in a culture can escape you otherwise, because you don’t know the rationale behind why things are done the way they are. One example from Japanese culture I always found interesting was that pouring drinks for your fellow diners while eating is considering good etiquette.
The concept might seem odd, if one has never been exposed to it before. Perhaps there are those that will read this and find the idea sound, and put it into practice when they dine out next, to examine if it fosters some camaraderie or other desirable result. Some might argue that doing so is disrespectful, labeling those that would try as cultural appropriators though I would disagree with this as a blanket assessment.
Sure, there are some that are disrespectful in their methods, though this is perhaps due to ignorance rather than malice. However, we have only gotten so far, so fast as a species because we dare to step outside of our comfort zones, and learn from the experience.