How do Christians who subscribe to the "religion vs. relationship" dichotomy make sure that their own relationship with God is genuine?

The two concepts can be contrasted in this way. Religion is about being seen and admired by men and relationship is about being known and loved by God. God complained about religiosity in Isaiah 29:13.

The Lord says: “These people come near to me with their mouth and honor me with their lips, but their hearts are far from me. Their worship of me is based on merely human rules they have been taught. NIV

Jesus elaborated on the concept.

MT 6:5 “And when you pray, do not be like the hypocrites, for they love to pray standing in the synagogues and on the street corners to be seen by others. Truly I tell you, they have received their reward in full 6But when you pray, go into your room, close the door and pray to your Father, who is unseen. Then your Father, who sees what is done in secret, will reward you

. There is a story in Luke 7 that illustrates the difference between religion and relationship.

36When one of the Pharisees invited Jesus to have dinner with him, he went to the Pharisee’s house and reclined at the table. 37A woman in that town who lived a sinful life learned that Jesus was eating at the Pharisee’s house, so she came there with an alabaster jar of perfume. 38As she stood behind him at his feet weeping, she began to wet his feet with her tears. Then she wiped them with her hair, kissed them and poured perfume on them.

39When the Pharisee who had invited him saw this, he said to himself, “If this man were a prophet, he would know who is touching him and what kind of woman she is—that she is a sinner.” 40Jesus answered him, “Simon, I have something to tell you.” “Tell me, teacher,” he said.

41“Two people owed money to a certain moneylender. One owed him five hundred denarii, c and the other fifty. 42Neither of them had the money to pay him back, so he forgave the debts of both. Now which of them will love him more?” 43Simon replied, “I suppose the one who had the bigger debt forgiven.” “You have judged correctly,” Jesus said.

44Then he turned toward the woman and said to Simon, “Do you see this woman? I came into your house. You did not give me any water for my feet, but she wet my feet with her tears and wiped them with her hair. 45You did not give me a kiss, but this woman, from the time I entered, has not stopped kissing my feet. 46You did not put oil on my head, but she has poured perfume on my feet. 47Therefore, I tell you, her many sins have been forgiven—as her great love has shown. But whoever has been forgiven little loves little.” 48Then Jesus said to her, “Your sins are forgiven.”

The Pharisee, Simon, may have been a very religious man and even practiced good deeds, but he was concerned about what others thought so he didn’t show much customary hospitality toward Jesus, knowing that his colleagues were not, to say the least, very favorably inclined toward him.

But the woman didn’t care about what anyone thought except for Jesus and she ministered to him with complete love and devotion. She was acutely aware of her need for a Savior and nothing was more important to her than a relationship with a man she could trust who would not despise her or take advantage of her. Jesus accepted her humble heartfelt request for relationship and forgave her sins.

Jesus sent her on her way with these words, “Your faith has saved you; go in peace.” Can you imagine the relief the woman must have felt having been able to pour out her heavy sin-laden heart to a compassionate and loving Savior? Her sins were forgiven and she was saved! What peace! What indescribable joy! That is one way we can know that we are having “a genuine relationship with the living God, as opposed to a 'religious' illusion”. We will experience his love, joy, and peace, the fruit of the Spirit, in our worshipful, grateful hearts.