Take Italian immigrants to America in the late 1800s
They arrive in droves, speak Italians, and consider themselves to be 'Italians' living in a different country.
The 'Italian' Cultural identity, made up of the perceived amalgomation of the 'Italian' citizenry still considers them to be a part of it.
As the immigrants become accultured to 'American' culture, the immigrants, 1 by 1 shift from being 'Italians who live in America' to 'Italian-Americans' who view themselves as a subgroup of 'American' culture.
The important elements :
1: A culture exists and has a name
2: People can leave a culture and join another
3: Cultures can change over time, without people leaving or joining.
4: Cultures represent the averages of their members, not hard values
Other things to think about:
Early Romans converting to Christianity: (Many mores changed, but not all, The culture conversions changed the country itself)
Outliers and Far-X groups. As group X starts to drift more extreme, the moderates decide to leave the culture, making the group even more extreme. Basically, you start alienating more and more people, until your group is just a couple of crazies. This mechanic could be used to start new movements with a charismatic leader. As time passes, the charismatic leader holds the mores to his mores. When he dies, the group starts to drift with the majority opinion of members (which was defined by the charismatic leader, so there's no snap when he dies). The group will either stay close to the middle (and gain lots of followers) or drift quickly off. Either way, the effect is a top, spinning about itself.