When faced with conflicting obligations in Islam, the principle of prioritization is based on the concept of necessity and importance. In such situations, the general guidance is to prioritize the obligation that is more crucial or necessary at that moment.
For example, if a person has to choose between attending a communal prayer (such as Friday prayer) and helping a family member in need, the duty towards family takes precedence because fulfilling the needs of family members is highly emphasized in Islam.
Similarly, if a person has conflicting obligations related to worship, such as performing the obligatory prayer (fard) and attending to a work commitment, fulfilling the religious duty of prayer would take precedence as prayer is a fundamental pillar of Islam.
Ultimately, the decision on prioritizing conflicting obligations should be made based on the principles of Islamic teachings, considering the importance, necessity, and impact of each obligation in the given circumstances. Consulting with a knowledgeable religious scholar or seeking guidance from Islamic sources can also provide clarity in making such decisions.