The younger son is like someone who takes God for granted and leaves to pursue his own ends
The older son is like a rather committed believer who is a little too closed-off about new believers
The father is... well, the Father
Like many of Jesus' teachings, this story has a lot more than just the surface interpretation. This is more than a story of a young man fleeing from home to indulge in all manner of sin and recklessness, only to head back to his father after famine strikes swiftly. Moreso, it is an allegory for God's children abandoning Him and His providence.
6 We all, like sheep, have gone astray, each of us has turned to our own way; and the Lord has laid on him the iniquity of us all.
Isaiah 53:6
Not only abandoning, but trading the creator of the Universe, and the literal embodiment of perfection, for a life of indulging in hollow desires of the flesh, and when the music stops and the partying ends, everyone who took part are left with nothing.
14 After he had spent everything, there was a severe famine in that whole country, and he began to be in need. 15 So he went and hired himself out to a citizen of that country, who sent him to his fields to feed pigs. 16 He longed to fill his stomach with the pods that the pigs were eating, but no one gave him anything.
Luke 15:14-16
The next part of the parable can be taken as a very discreet rebuttal to the false idea that detracts many people from Christ: the thought of God being angry and vengeful towards non-believers as they seek Him. The following rejects that claim:
20 So he got up and went to his father. “But while he was still a long way off, his father saw him and was filled with compassion for him; he ran to his son, threw his arms around him and kissed him. 21 “The son said to him, ‘Father, I have sinned against heaven and against you. I am no longer worthy to be called your son.’ 22 “But the father said to his servants, ‘Quick! Bring the best robe and put it on him. Put a ring on his finger and sandals on his feet. 23 Bring the fattened calf and kill it. Let’s have a feast and celebrate. 24 For this son of mine was dead and is alive again; he was lost and is found.’ So they began to celebrate.
Luke 15:20-24
This final part retells the premise of the Parable of the Vineyard. You shouldn't be offended that salvation is offered the same to the sinner and the saint. As a reference point, here's what it says in The Parable of the Vineyard:
8 “When evening came, the owner of the vineyard said to his foreman, ‘Call the workers and pay them their wages, beginning with the last ones hired and going on to the first.’ 9 “The workers who were hired about five in the afternoon came and each received a denarius. 10 So when those came who were hired first, they expected to receive more. But each one of them also received a denarius. 11 When they received it, they began to grumble against the landowner. 12 ‘These who were hired last worked only one hour,’ they said, ‘and you have made them equal to us who have borne the burden of the work and the heat of the day.’ 13 “But he answered one of them, ‘I am not being unfair to you, friend. Didn’t you agree to work for a denarius? 14 Take your pay and go. I want to give the one who was hired last the same as I gave you. 15 Don’t I have the right to do what I want with my own money? Or are you envious because I am generous?’ 16 “So the last will be first, and the first will be last.”
Matthew 20:8-16
Now here is a similar lesson being presented in the form of the the older son:
29 But he answered his father, ‘Look! All these years I’ve been slaving for you and never disobeyed your orders. Yet you never gave me even a young goat so I could celebrate with my friends. 30 But when this son of yours who has squandered your property with prostitutes comes home, you kill the fattened calf for him!’ 31 “ ‘My son,’ the father said, ‘you are always with me, and everything I have is yours. 32 But we had to celebrate and be glad, because this brother of yours was dead and is alive again; he was lost and is found.’ ”
Luke 15:29-32
This theme is timeless, as is the rest of Scripture. Anyone, regardless of the era, or social status, knows the struggle of finding yourself engaging in sin, straying far from God and Christ leading you back. It is a universal story that plays out in every believer's life.