Your culture isn’t the only one on the earth today and we should all rejoice. The various cultures all add to the beauty of the mosaic of God’s family.
Repentance is a theology, response, act, and is cultural too. People show the signs of repentance in different ways. One culture encourages tears with repentance while another encourages stoicism.
Most of the Old Testament cultures include outward signs of deep, contrite repentance. Maybe most common among the outward signs of repentance are sack cloth and ashes.
Today, with ashes on my forehead, I join the Old Testament cultures inn repenting of sin.
Tomorrow, if I were to join your culture with an outward sign of repentance, what would I do?
With some, I would weep. With others I would give sacrificially. Yet with others I would make restitution.
It seems to me that outward signs of repentance can be good, within reason. The Old Testament required a sin offering. Of course, Jesus is the sin offering, but that may serve to inspire us to make repentance visible and then produce fruit in keeping with repentance.