Existentialism or the natural sciences alone cannot fully explain reality and does not have complete authority over all other interpretations of life. There are many other fields of inquiry that help to interpret reality. Such as reason the laws of logic, which is a great key component and field of inquiry that helps to acquire knowledge and interpret reality.
The laws of logic are absolute, non-observable, universal, transcendent, abstract, immaterial, unchanging and self-evident. They cannot be proven scientifically, yet we all use them when we reason. They apply repeatedly in the realm of contingent experience. They cannot be avoided or accounted for in a naturalistic or materialistic universe.
Now consider the Christian Biblical worldview in contrast to any other perspective… It is unique in all systems of thought and world religions because it's not rooted in a set of ideas, it's not rooted in a set of experiences and it's not rooted in a way of life. It's rooted in the person of Christ.
Christianity is not either epistemological (rooted in knowledge), it's not existential (rooted in experience), it's not pragmatic (rooted in doing). Christianity is ontological. It's rooted in "being".Knowledge comes to us in words. Words are the tools in thinking. Words are revealed thought. Words reveal thoughts of the person who is speaking. It is through someone's words that you can begin to understand what they're saying. In the Gospel of John 1:1, it says that "the Word became flesh… and dwelt among us."
Christ came and said that you don't even have life until you know me. He defined life in terms of knowing him. Christ said that he didn't come to give us a new experience in life , but rather the experience of life itself.
The pursuit of truth ultimately requires some struggle with other philosophical worldviews a person may be comfortable with or emotionally attached to.
That is why if an honest skeptic remains intellectually honest, the problem is not the struggle with intellectual doubt, but instead the limitations (most probably) by the moral constraints put forth by a Christian Biblical worldview.