In my country, Christians are no longer a majority (they are the largest religious group). Chaos has so far failed to ensue.Religion also encompasses community and community expectations. Parenting has a huge influence on behaving ethically.
Across the Baltic sea, the Scandinavian countries are largely secular. Likewise, the rule of law and the ethical behavior of the inhabitants are not in danger.
Parenting and community life are not dependent on religion. We have libraries, schools, theaters, sports clubs, art studios, street markets, self-organized community centers (secular), and yes, religious communities. The latter do not hold a monopoly on moral fortitude, as far as I can tell.
How about your community?