Is not carrying one's civil ID and driver's license when leaving the house considered a form of complacency and lack of reliance on Allah?

Taking lawful means does not contradict reliance on Allah (tawakkul). The Prophet, peace and blessings be upon him, took means in his battles and his emigration, and commanded the one who asked him to tie his camel and then rely on Allah.

Therefore, carrying identification cards, if it is a requirement according to the country's laws, is permissible, while believing that preservation and safety come from Allah is what is incumbent.