For me, the phrase "when in Rome, do as the Romans do" never applied more than living in the Czech Republic. As an American, I became acutely aware of "Americanisms" that are not as common in Czech. For example, in my experience, shaking hands when meeting someone happens here but really mostly in a business setting. Another example is Americans' habitual greeting of "how are you?" when in reality, that is not a sincere question and the asker doesn't really care what the answer is nor do they want to hear anything more than a ubiquitous response like "fine" or "couldn't be better" etc. Americans also have an irritating habit of smiling all the time, I am not sure where this comes from; it isn't that we're all insufferably happy and I don't recall ever being taught or told to smile all the time. Conversely, Czechs do not smile all the time by default and it's what has led to their perception as a dour or icy folk when in reality, now that I have many close and dear Czech friends, they smile more broadly and warmly than any Americans I know - they just only do it when they're actually feeling joy and happiness, not just because they want a latte or see a stranger on the street.
I think Czechs are more sincere with their feelings, whether good or bad and I think Americans are conditioned to not be a "Debbie Downer" in social situations so either be happy or act happy at all costs, is what I see in the USA but not here. Czechs are also big on sincere eye contact, and one of my very favorite things here is how a group will toast over drinks. Even if it's just a bunch of guys getting beer, the first toast, everyone makes sure to clink the glass of everyone else and at the moment of the clink, direct eye contact and acknowledgment is made.
Learn about and be aware of Czech's history and how it affected generations of people and molded them into who they are today. If you are American, you'll find more people happy to meet you in the west than in the east, and history post WW2 can explain why. The US and the USSR brokered a deal that divided Europe and many in the older generation that remember this still aren't too happy about it as they had to suffer for a long time, and there is some blame placed on the US still. Czech had many long periods of suffering over centuries, and subsequently, Czech is one of the least religious countries on the Earth. When asking Czech friends about this, I always get a similar response - that their faith went unrewarded for so long, they simply gave up. Not to say that there aren't some religious Czechs but statistically, Czech has by far the highest percentage of agnostic/atheist or secular (undefined) religious beliefs in the world. Subsequently, if you are religious, it's probably best to keep that to yourself unless asked about it.
One last observation is that compared to Americans, Czechs are generally peaceful caring warm people who just want to live their lives in peace. While standout citizens (sports icons, actors, artists, etc) are honored, I don't see the same ravenous gluttony and striving for stardom as I see in America where teenage girls dream of being a Kardashian or being on TV all the time, seeking their 15 minutes of fame. Czechs don't appreciate controversy or discord and in my experience, are not keen to discuss global politics, religious differences or current events the way Americans are. One negative aspect in my opinion is that I think Czechs aren't very fond of cultural differences in general. I'm not generalizing and I know some Czechs who are very open to the bigger world and the fact that most of it is not very Czech but the vast majority of Czechs I know, while polite and quietly appearing tolerant of cultural, ethnic and social differences, in fact would prefer that their society remain as it has been with minimal outside influence. Whether this indicates the level of acceptance or non-acceptance of Muslims, people with darker skin, people who speak a different language, the LGBT community, etc. As a straight white male American married to a Czech woman with Czech-American kids, I blend in better than most and I am not sure I would be as happy here as I am if I were a gay black woman. But this circles back to my initial statement - when in Rome, do as the Romans do, and when in Czech, accept that this is the way Czech is and for those who don't like that or don't fit in, this probably isn't the best country for you to seek broad levels of appreciation for diversity.
Just thoughts from a guy who's lived here about 10 years.