JOEL - You are right about the significance of the veil being torn at the death of Jesus. Some believe that the rending of the veil signified the rending of Judaism and the end of the Mosaic dispensation, bringing about the beginning of Christianity under apostolic administration. Some see the rending of the veil as a solemn act of mourning on the part of the house of the Lord. In the East men express their sorrow by rending their garments; and the temple, when it beheld its Master die, seemed struck with horror, and rent its veil.
For many generations only the high priest had been permitted to pass through the veil of the temple, which symbolized entering the presence of God.
But through his death, Jesus rent that partition, signifying that all people could reach God’s presence if they wanted to. The atonement, death, and resurrection of Jesus gave everyone the opportunity to enter into God's kingdom whereas before this time it was not even possible. However, to take advantage of this opportunity there are certain things we need to do as Jesus explained in Matthew:

"Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven." (Matthew 7:21)

Even though, because of Jesus, we now have the opportunity to enter God's Kingdom, we won't get there unless we do the will of the Father.
Even though the atonement of Jesus makes it possible for everyone to receive forgiveness of their sins, that is not going to happen unless we repent and forsake our sins.
Following the same logic, even though everyone now has the opportunity to enter the Temple of God and pass through its veil, we can not be allowed to unless we are worthy to do so, because no unclean thing can enter the House of the Lord.(1 Cor. 3:16-19, 2 Chronicles 23:19, D&C 109:20)
A scripture in Alma says:

"And he doth not dwell in unholy temples; neither can filthiness or anything which is unclean be received into the kingdom of God;" (Alma 7:21)

You said that your father believes "that the tearing of the veil in the temple clearly shows that anyone may enter the temple". But that was already the case even before Jesus died. Before the veil was torn almost anyone could go into the temple:

"And early in the morning he(Jesus) came again into the temple, and all the people came unto him; and he sat down, and taught them."(John 8:2)

Even the disrespectful moneychangers were allowed to go in:

"And Jesus went into the temple of God, and cast out all them that sold and bought in the temple, and overthrew the tables of the moneychangers, and the seats of them that sold doves," (Matthew 21:12)(See also 2 Kings 11:13)

The main restriction was that no one could go past the veil into the "Holy of Holies" into the presence of God. I think the better interpretation is what I explained above. That it symbolized that, because of the sacrifice of Jesus and His atonement and resurrection, everyone now had the opportunity to enter the presence of God in His kingdom if they repent and keep His commandments..