Augustine of Hippo (354-430) did not live in the Age of Science, as we do today. Nor was the word 'science' yet coined in any language, so any translation of his words which pops in 'science' is not using a word he would have used. Translators are sometimes at risk of assuming that a word we use today is equivalent to an ancient one, as in Latin or koine Greek or biblical Hebrew. That has happened with our comparatively modern word 'science', which we now take to mean a disciplined methodology to discover how things in the natural world 'work', proven by repeatable experiments. (I know that's not a dictionary definition, but I wish to make a point.)
So, what did Augustine refer to, in that quote? Here is another one from the same book. From this, we can grasp what he had in mind when modern people have in mind scientific, verifiable experimentation:
"Usually, even a non-Christian knows something about the Earth, the
heavens and the other elements of this world... Now, it is
disgraceful and dangerous thing for an infidel to hear a Christian,
presumably giving the meaning of Holy Scripture, talking nonsense on
these topics... People outside of the household of the faith think our
sacred writers held such opinions, and... if they find a Christian
mistaken in a field which they themselves know well and hear him
maintaining his foolish opinions about our books, how are they going
to believe those books in matters concerning the resurrection of the
dead, the hope of eternal life, and the Kingdom of Heaven?" The
Literal Meaning of Genesis, Vol. 1, translated by J.H. Taylor (New
York: Paulist Press, 1982)
There he has in mind knowledge of the Earth, the heavens, and elements of this world. This quote agrees with the one given in the question. In his day, and up until the coining of the word 'science', the phrase 'natural philosophy' would have been used. In this related quote, Augustine has in mind the way in which the natural world functions as a system of signs. We would call that 'semiotics' today, but that modern word will no more be found in Augustine's writings than the word 'science'.
"Some people read a book in order to discover God. But there is a
greater book - the actual appearance of created things. Look above and
below you, and note and read. The God that you want to discover did not write in letters of ink, but put
in front of your eyes the very things that he made. Can you ask for a
louder voice than that?" Sermons 68, 6, Augustine of Hippo
Those two quotes show how - in what sense - Augustine warned about interpreting any books about natural philosophy in a way that shows up Christian ignorance on the topic. He advocates looking at the "book" of God's creation which is visibly all around us, to "find" (by observation) what can be known of God there. He even gives the impression of considering the natural world to be more powerful a witness to God than the written Holy Scriptures!
The answer is the other way around to how it's posed in the question. Augustine was concerned that Christians uttering nonsense about the known natural philosophy of his day would prevent non-Christians from then listening to them about biblical doctrines such as "the resurrection of the dead, the hope of eternal life, and the Kingdom of Heaven"