IPA: /nɒn.rɪˈlɪdʒ.əs/
KK: /nɑnˈrɪdʒ.əs/
Not connected to any religion; relating to secular matters.
The school promotes a nonreligious environment where all beliefs are respected.
Nonreligious → It is formed from "non-" (meaning not) and "religious" (from Latin "religiosus", meaning devoted or pious). The word "nonreligious" means not devoted to or associated with religion.
Think of 'not' ('non-') being combined with 'devoted' ('religious') to remember that 'nonreligious' refers to something that is not associated with religion.