It can be pretty scary mixing with non-Christians who seem to have thought through their opinions fairly deeply and who hold them very firmly. When professors seem to give weight to anti-Christian thinking this can be particularly hard. We begin to fear that the gospel will sound ridiculous, and so never speak about Christian things.
There are several things that we need to meditate upon.
i) We should not be surprised that people will use their whole intellect to oppose the gospel. Even the apostle Paul says of himself before his conversion, “I too was convinced that I ought to do all that was possible to oppose the name of Jesus of Nazareth”. (Acts 26:9)We need to recognize though that people’s opposition to the gospel is not primarily intellectual. It is moral stand against the Lordship of Christ dressed in an intellectual garb. The converting work of the Holy Spirit is well able to show people the folly of that stand, and it is as the gospel is shared even by fearful students that this will be happening on campus.
ii) It is as we fear the Lord more we can fear others less and love them more. If we are paralyzed by the fear of man it will stop us from loving them enough to share the gospel – their only hope for salvation. If we are gripped by the fear of the Lord, we will seek to honour him in declaring the Lordship of Christ, and the result will be a gentle, loving, compassionate sharing of the gospel with those who are lost. If we really fear the Lord, we will fear nothing else but will be content even in the face of great opposition. (Proverbs 19:23)
iii) Opposition to the gospel is well addressed in Scripture. Meditate of those passages in Scripture that hold out to us our eternal hope. They are intended for all who suffer – not just those suffering more than we do! (1 Peter 3:13-18) For more on suffering, see John Piper's reflections (HT: Justin Taylor)
iv) There is in the end no need to fear someone who is unable to remove our faith. Sharing the gospel will only ever strengthen faith. Our confidence that we will be kept in the faith is not in our ability to convince someone of the truth of the gospel (we have no such ability!) It is in the God’s committed sustaining love for us. He has already shown us just how committed he is by sending his Son. (Romans 8:31-38)
A great book to read to meditate more on overcoming the fear of man is Ed Welch's When People are Big and God is Small.