Paul is not ashamed and I am not ashamed either. The part about this verse that is often overlooked is that the gospel contains the power of God. The implications are that the power of God provides to the believer :
- power through prayer (healing, salvations, miracles)
- prophesy and interpretation of prophesy
- words of knowledge
- communication with God
- forgiveness of sins
- short term and long term blessings
- visions and dreams of things to come
- interventions by God into your daily affairs
The point is that those who do not believe the gospel do not have access to any of these spiritual components. Some people think they do. There are people all over the world who call themselves spiritual without accepting the Lordship of Jesus Christ. And from one perspective those who do not believe the gospel can dabble in spiritual things. Because every human was made in the image and likeness of God there is an inherent internal desire to know God and to operate in the spiritual realm. However, without the power of the gospel, there is no direct connect with God. There is however direct connect to the demon world.
That's really the big difference in the ability of believers to ward off evil influences. Believers have the power of God to use against the wiles of the wicked, non-believers do not have this power. That doesn't mean that there are not good people who do not believe the gospel. There are many good people who do not believe in or trust in Jesus. There are even good people who do not acknowledge the existence of God. But don't think for one minute that they enjoy the benefits of having personal relationship with God, nor do they inherit the benefits of the afterlife.
All the power of God is in the gospel of Jesus Christ.