It seems that you are implying that there could be some substantial difference between religious authority and non-religious authority when it comes to justification. But there isn't.
Ultimately, whatever justification you use will fall back to an endless loop of requiring justification unless you hold something to be true which itself does not require justification outside of itself.
Science is no exception. It requires a vast amount of assumptions before it can even operate (uniformity of nature, adequate ability to reason, ability to trust our empirical senses, and so forth), and those assumptions must either be justified or held without justification. In essence, science also requires some authority. For example, many people who claim to trust in science, knowingly or unknowingly, subscribe to Scientism to fill that void. Others use theistic religions to rationally justify the metaphysics required for science and the impetus to perform science, such as those thinkers who gave us modern science.
So, the question then becomes "Which authority is best justified?" We cannot know what is true, undeniably, but we can perhaps know some things deductively. For one thing, if we presume that we can accurately reason, then whatever justification we use has to justify our ability to reason. Each claim should be analyzed individually along with the source and the reliability for the method. Once you have a basis for justification, then you can perform inference grounded in that.
Some beliefs can be discarded for internal inconsistencies. Others don't provide sufficient impetus or predictive ability. None can be rejected offhand and there is no default. Each must rest upon its own merits and implications.