The pure (clean) virgins are not cast out.
No, the foolish virgins are cast out:
Matthew 25
King James Version
1 Then shall the kingdom of heaven be likened unto ten virgins, which took their lamps, and went forth to meet the bridegroom.
2 And five of them were wise, and five were foolish.
Nothing about clean and unclean animals, but five wise and five foolish virgins.
In view is The Kingdom of Heaven, and what it is likened to.
11 Afterward came also the other virgins, saying, Lord, Lord, open to us.
12 But he answered and said, Verily I say unto you, I know you not.
Being known of the Lord is a familiar concept, as is not being known of the Lord (Matthew 7:23; 2 Thessalonians 1:7-9), and it always speaks of those who are rejected by God because they rejected God Himself.
They are not making the grade of the Master's gaze, and are therefore not able to partake of the high place of the wise virgins.
That sure is a nice way to put being refused entrance to the Kingdom.
They, however, are pure virgins!
I see nothing in the text to indicate "pure virgins," only that they are foolish and are refused entrance to the Kingdom when Christ returns.
Regarding the two clean animals,
There are no two clean animals in the text.
Just another wresting of Scripture as an attempt to rationalize universal salvation. And it simply doesn't fit the teaching.
I suggest you concentrate your attention on the Old Covenant listing of clean & unclean animals.
Why not concentrate on the Old Testament teachings that would be relevant to this teaching?
Such as the gathering of the Nations for judgment?
Isaiah 66:23-24
King James Version
23 And it shall come to pass, that from one new moon to another, and from one sabbath to another, shall all flesh come to worship before me, saith the Lord.
24 And they shall go forth, and look upon the carcases of the men that have transgressed against me: for their worm shall not die, neither shall their fire be quenched; and they shall be an abhorring unto all flesh.
"All" come to worship the Lord, but not all of them will be alive. This speaks of Christ's Return. And it is an Old Testament basic knowledge that the "All" refer to those who have been redeemed of the Lord.
Christ gives this Prophecy an eternal context in His teachings:
Mark 9:43-44
King James Version
43 And if thy hand offend thee, cut it off: it is better for thee to enter into life maimed, than having two hands to go into hell, into the fire that never shall be quenched:
44 Where their worm dieth not, and the fire is not quenched.
Both sheep & goats are clean animals!
Not in Matthew 25.
Sorry, but sheep and goats represent believers and unbelievers. Most people can see that and don't try to rationalize the text to wrest its meaning.
These (clean animals & virgins) shall go into aionios kolasis.
Actually, it is pretty clear that it is the unbelievers only that go into everlasting punishment:
Matthew 25:46
King James Version
46 And these shall go away into everlasting punishment: but the righteous into life eternal.
Only the righteous will enter into Eternal Life.
Just as Christ also taught here:
John 3:3
King James Version
3 Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God.
We have been given the New Testament to understand the New Covenant promised to Mankind beginning in Genesis 3:15. Trying to merge and blend teachings might convince those who have no sincere desire to understand God's will for man, but it isn't going to deceive sincere Bible Students.
You can seek to impose your teaching into this passage all you like, but it isn't going to change what for most is easily discerned.
God bless.