When truth and loyalty are in conflict, have the wisdom and courage to decide what to do. Loyalty must be based on your own set of values.
Being loyal to someone should not mean closing your eyes to their faults. Loyalty should not mean blind faith. It should be an ongoing reality check not only for your own benefit but also for those we profess loyalty towards.
Similarly, loyalty to religion and politics is good as long as it helps you relate to people. The ideas must be re examined in the new light, as what adheres to us at the age of 13 may not be really be valid till you reach 50. But don't confuse loyalty with obedience.