The absolute necessity of the new birth can be seen in a type. The law of God distinguished between clean and unclean animals — the unclean could not be offered in sacrifice. From this, some might want to infer that any clean animal could be so offered, but this was not the case at all. An animal could belong to the category of the clean, and yet still not be fit for sacrifice. The weak and infirm animals could not be offered, the animals with a blemish could not be, and so on.
When we come to worship God, we come to offer ourselves. If someone is baptized, this means he is a sheep, not a dog. But more is required than “not being a dog.” When a priest was examining an animal presented for sacrifice, his work was not done when he ascertained that it was not a dog.
And of course, the final gospel answer is that we are all of us maimed, and the only perfect sacrifice was that offered by the only clean victim. If we are in Him, then His perfections are ours. If not, then our imperfections remain our own — even if we have been removed by baptism from the category of the unclean.
A blemished sheep in sacrifice can no more be accepted by God than a pig.