Cultural differences—ones we adopt or are born into—are part of what define us. For a character who understands this, losing that aspect of their identity can shake the foundation of who they are and threaten the deep connections they have with others from their culture. This is an enormous loss. While it's normal and healthy to nurture one's heritage for oneself and one's family, a fear of losing that sense of identity—whether the possibility is real or perceived—can drive the character to great (even unhealthy) lengths to keep it from happening.

Holding firmly to personal traditions
Observing cultural rituals to keep them alive and relevant
The character educating their children about their culture: engaging in traditions, telling them stories about their heritage, speaking their native language at home, etc.
Seeking to educate others about the character's culture—forming a club at school or a committee at work, for instance
Becoming an activist
The character seeing offense or slights against their culture where none were intended
Refusing to assimilate or integrate into a different culture
Living a life at home that looks different from the character's life outside of the home
Only associating with people within the character's cultural group
The character sheltering their children from influences outside of their community
The character unintentionally passing their fear of others to their children
Requiring loved ones to choose spouses from within their cultural group
Scorning those outside of the character's community (rejecting them before they can reject the character)
Developing an us vs. them mentality