"First, the Protestant notion of the Cross & Atonement (what they call "Penal Substitution") is that a sinner's guilt is 'imputed' to an innocent substitute, which then takes the death penalty in place of the sinner. But in this case, what was Mary's (grave) "sin" here that had the death penalty hanging over Her head, which She had to then transfer onto two turtledoves? The obvious issue here is that Mary had given birth to the Messiah, Jesus. But this certainly was not a sin in any sense. Thus, Mary's sacrifices couldn't have been about imputing the guilt onto an innocent animal substitute, much less was the animal receiving the death penalty. Thus, an animal being killed in sacrifice should not be assumed to be modeling Penal Substitution."
"That said, a Protestant might object at say that this Mary situation doesn't affect Penal Substitution at all, since some sacrifices weren't about atoning for sin but rather simply about ritual purification. While there is truth to this claim, this Protestant "objection" actually backfires. The passage which Luke is referencing is Leviticus 12, a short chapter on childbirth ritual purification. The plain fact is, Leviticus 12:6-7 explains it as "a turtledove for a sin offering, and the priest shall offer it before the Lord and make atonement for her. Then she shall be clean from the flow of her blood." Notice the explicit mention of "sin offering" and "make atonement". This is yuge because it means the sacrifice Mary had offered was not something distinct from the standard "sin offering" which Leviticus 4-5 tells us about. In other words, this is clear proof that "sin offering" and "making atonement" don't need to involve Penal Substitution."
Leviticus 12 does refer to ritual purification, but that does not mean that it is completely divorced from moral disobedience. Atonement for sin is still necessary because the ritual uncleanness comes from our own fallen disobedience. It would be quite a mistake to always link individual sins to individual sacrifices. The world is fallen in general because of our own sin.
"Note that Leviticus 12-15 are about various types of ritual purification, not having to do with guilt for actual sins, yet all involving "sin offering" to "make atonement". Also noteworthy is that these purification chapters come, right before Leviticus 16, which is the Day of Atonement ritual (centered on purification)."
Leviticus 16 records Moses warning his brother Aaron to not violate the code of holiness by offering strange fire, lest he undergo the same fate as his sons Nadab and Abihu. The two were struck down brutally by God (Leviticus 10). The aversion of divine wrath can clearly be seen in Leviticus 16. The prescribed rituals were indeed related to propitiation.
The guilt which is a result of sin is transferred from the Israelites to the animals themselves. Their innocent blood was shed by priests on account of the people. Jesus Christ expiates, cleanses, and removes our sin from us. The Day of Atonement prefigured His work on the Cross.
"This "their purification" detail is noteworthy within this discussion because some Protestants have tried to use this passage as proof that Mary was a sinner and needed cleansing. But because the term "their" is used, it then means that Jesus is now part of this sacrificial ritual, and we know that Jesus was certainly without sin. So if Jesus was undergoing it yet had no sin, then it means Mary didn't necessarily have sin just because She was also undergoing this purification. Many Catholic theologians have noted that Jesus and Mary followed the Mosaic Law even though they weren't strictly bound to certain parts (Gal 4:4-5). Catholic apologist Joe Heschmeyer speculates: "I suspect that the two spotless birds represent Jesus [sin offering] and Mary [burnt offering] – who, like the birds in Leviticus 12, are innocent, yet brought under the Law for the good of sinners."
All this proves is that Mary and her household was faithful to the Law. If Jesus Christ was sinful, then that would mean He is not qualified to bear our sin in the first place. Christ had no biological father. The point in asking why Mary needed to offer a pair of turtledoves or young pigeons is to illustrate how she is nowhere in Scripture elevated in the manner that Roman Catholics do with her. She is just like every other woman.
If Mary herself was undefiled by sin, then there would have been no reason for her to make any sacrifice in the first place. Her undergoing a ritual of purification would have been simply redundant and arbitrary. The idea of Mary being sinless is unscriptural and has no practical theological necessity.
Certainly, the worship of God was a part of the sacrificial system. However, atonement was front and center by the constant shedding of animal blood.
The firstborns are targeted because it is a general biblical principle that you give the first fruits to God. A substitute was required because God did not want the Israelites to practice child sacrifice. It does not have anything to with penal substitution. At times, sacrifices can be expressions of worship. This provided for the priests and Levites. The Apostle Paul picks up on this language in Romans 12 where he teaches that believers should offer themselves as sacrifices for worship. It is a sacrifice of worship. This not a denial of penal substitution in the Old Testament. It is just teaching that at times sacrifices were simply expressions of worship.
The laws pertaining to the priesthood, tabernacle, sacrifice, etc., were ceremonial. The fact that Christ's parents, in fulfillment of their duties under the Law, followed the Mosaic prescriptions does not indicate that Jesus was a sinner or needed redemption in that sense. Scripture is clear that Jesus was without sin.