As taught to me by my Acharyan, the color white is universally considered a symbol of peace. The twin feet of Our Lord give us peace so we wear them on our forehead to invoke that in us.
Red is universally the symbol of love, kripa. We are because of His love. We are constantly reminded of that by wearing that. So, our way is of Love and Peace.
Please recognize that this is the explanation from a Jeeyar.
This is also source link which says the same.
