I'm sure it works out fine except for that minority that doesn't want to look the same and think the same. Give me diversity every time. Nonconformists are the ones who move society forward. I'm surprised to hear you championing conformity, TBH.
Here's to the crazy ones.
The whole basis of a nation-state is a state united by a single culture and/or ethnicity. I think it's a perfectly valid archetype for a state.
In a culturally and ethnically homogenous society, societal change is essentially equivalent to cultural change, which still happens. You still have non-conformists who change society, but the clashes tend to be between different age groups, as the needs and values of society change from generation to generation. See the age gap in Japan, for example.
Of course, I think minorities who don't identify with the culture and ethnicity of a nation-state should be free to form their own state. And this is where modern concepts of land rights, property rights, and other geopolitical boundaries tend to get in the way. For example, I think both Israel and Palestine have a right to exist and to Jerusalem, but sharing it is very difficult in today's political climate, with our current concepts of ownership and geopolitical boundaries.
I also value diversity, but it certainly makes governance more difficult, and I think (ethnic/cultural) nationality is an entirely valid way to make a state. A lot of issues get a lot simpler (but still complicated) when everyone is coming from the same cultural/ethnic background and shared history.
It's certainly not perfect, but nothing is.
Incidentally, I also have no problem with such things as a state religion, in theory. But like many other things, it's not right for the US. Likewise on gun bans. I have no problem with them philosophically, but I don't think they'd work for the US.
Fortunately, I have dual-citizenship to both kinds of setups, so I don't have to choose only one.
