Denying the Good News
Of course, the most common way (among so-called "professing Christians") of rejecting the true gospel is believing that Christ's atonement was not 100% efficacious. That is, many say they believe Jesus "died for everyone" and that His death did not guarantee salvation. This is a false gospel.
The true gospel is that Jesus did everything necessary to secure the salvation of His people. All those for whom Jesus died will be saved. God's Spirit will grant genuine faith and repentance to all those whom Jesus represented.