Q — Is it acceptable to call Joseph the father of Jesus, especially since Luke: 2:33, and 2:48 refer to Joseph as the father of Jesus?
A — To reply to the question it may be useful to turn first of all to the two verses of Luke 2:33, 48. Verse 33: “And the child’s father and mother were amazed at what was being said about him.”
The context is the presentation of the child Jesus in the temple by Mary and Joseph, and the prayer of Simeon. Verse 48: “When his parents saw him they were astonished; and his mother said to him, ‘Child, why have you treated us like this? Look, your father and I have been searching for you in great anxiety.’” The context is the finding of the child Jesus in the temple after three days search.
It seems to me that the key word in your question is the word “acceptable.” What exactly does “acceptable” mean, and what is its intention? Among Catholics and traditional minded Christians generally, St. Joseph is not the biological father of Jesus.
According to the infancy narratives of St. Matthew and St. Luke Jesus is conceived by the blessed Virgin Mary through the power of the Holy Spirit and without male agency. In the scholarly literature on these matters Joseph is often referred to as the “father” of Jesus. In those scholarly milieux some scholars accept that that means “foster-father,” while other scholars accept it in the biological sense of the word. If one thinks with the church, calling Joseph the “father” of Jesus Christ, where “father” means “biological father” would be unacceptable.