Integrity requires that we never compromise on matters of moral principle. In some situations we may have to reconcile multiple principles that appear to point toward different courses of action, but this process is based on loyalty to principles, not the compromise of them. In the long run, compromise of valid moral principles always operates to the practical disadvantage of those who (halfheartedly) support those principles:

Since the good is based on an objective view of reality, and since that reality can be grasped only through principles, any action or position that obscures those principles, either in one's own mind or in the minds of others, will tend to work against the good.
On the other hand, since evil requires an obscured view of reality, it depends on the evasion of principles that might shed light on that reality. Thus any action or position that obscures moral principles will strengthen the hands of those who knowingly or unknowingly seek what is evil.