To be ashamed of Jesus means to be unwilling to be identified with him. It is an unwillingness to follow him, an unwillingness to be known publicly as his disciple. If the crowds allow the shame of being known/identified with Jesus to keep them from him, then Jesus will disown them when he comes in glory.1
To assert that the eternal destiny of all humans depends on their relationship to Jesus is a fantastic claim. Jesus can make this claim because he is the Son of Man of Daniel 7:13 who will soon die for the sins of God’s people.2
38 For whoever is ashamed of me and of my words in this adulterous and sinful generation, of him will the Son of Man also be ashamed when he comes in the glory of his Father with the holy angels.”