How do people who reject transubstantiation (but believe in sola scriptura) interpret these verses and still refute transubstantiation?

The John chapter six verses are difficult and many abandoned Jesus when they heard them. Even when Jesus asked the disciples if they would leave also, Peter responded;

John 6:68 Then Simon Peter answered him, Lord, to whom shall we go? thou hast the words of eternal life.

In context chapter six starts with Jesus feeding the multitude. This was so well received that there was every danger of the crowd making Jesus into a king. The next day some of the crowd catches up with Jesus and he tells them;

John 6:27 Labour not for the meat which perisheth, but for that meat which endureth unto everlasting life, which the Son of man shall give unto you: for him hath God the Father sealed.

This begins a long discussion where people do not understand his metaphor.

John 6:31-33 Our fathers did eat manna in the desert; as it is written, He gave them bread from heaven to eat. Then Jesus said unto them, Verily, verily, I say unto you, Moses gave you not that bread from heaven; but my Father giveth you the true bread from heaven.
For the bread of God is he which cometh down from heaven, and giveth life unto the world.

The key to the metaphor is the similarity of the physical life sustaining property of bread compared to the eternal life sustaining effect of faith in Jesus. There is also an implied metaphor in that bread is taken in by eating and that in a similar way the words of Jesus should be taken with just as much faith and enthusiasm.

Jesus clarifies by specifically declaring that the "life" obtained is through faith and not digestion.

John 6:40 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and I will raise him up at the last day.

Jesus even goes on to explain that only those who have been "drawn" are going to understand.

John 6:44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.

Jesus placed a strong emphasis on the metaphor but still ties it to abiding (dwelleth) in Christ and he in us;

John 6:54-56 Whoso eateth my flesh, and drinketh my blood, hath eternal life; and I will raise him up at the last day. For my flesh is meat indeed, and my blood is drink indeed. He that eateth my flesh, and drinketh my blood, dwelleth in me, and I in him.

Jesus is almost dismissive of the physical bread and the life is sustains;

John 6:63 It is the spirit that quickeneth; the flesh profiteth nothing: the words that I speak unto you, they are spirit, and they are life.

This brings to mind another "bread" analogy;

Luke 4:4 And Jesus answered him, saying, It is written, That man shall not live by bread alone, but by every word of God.

The whole of the sixth chapter of John is a contrast of physical bread and physical life with heavenly "bread" and eternal life.

As regards the last supper, the "bread" metaphor is used again this time to both illustrate that he is about to be "broken" himself and establish a memorial practice.

Luke 22:19 And he took bread, and gave thanks, and brake it, and gave unto them, saying, This is my body which is given for you: this do in remembrance of me.

The wine is illustrative of blood. The disciples were familiar with the many references in the Old Testament of life being in the blood. Also that the first covenant (testament) with Israel was established with the shedding of blood.

Exodus 24:8 And Moses took the blood, and sprinkled it on the people, and said, Behold the blood of the covenant, which the LORD hath made with you concerning all these words.

Jesus was announcing that the cup was representing his blood which was about to be shed as the establishment of the new covenant that Israel had been promised.

Jeremiah 31:31-32 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD:

Luke 22:20 Likewise also the cup after supper, saying, This cup is the new testament in my blood, which is shed for you.

To consider transubstantiation I think is to limit the context and implication of both John chapter six and the events of the last supper.

If a person is to understand the Word of God as He intends, he or she must read what the authors wrote as they intended it. If a passage was written as literal history, we should take it as literal history. If it's personal opinion, it's personal opinion. If it's allegorical, metaphorical, or poetic, we should take it as allegory, metaphor, or poetry.

So, what does the Word of God say about the Lord's Supper?

Transubstantiation refers to the changing of the elements of Communion (bread and wine) into the Body and Blood of Christ. That is not supported by Scripture.

The Word of God does state that Christ took the bread and wine and declared, "This is My Body; this is My Blood."

So, if a Christian is to take the Son of God at His word -- without adding to or deleting from it, sins against which Scripture warns vigorously -- then all he can say is that in the Lord's Supper, a Christian receives the Body and Blood of Christ (along with the bread and wine).

A changing of the elements into Christ's Body and Blood at a certain point (when the priest consecrates the elements, for example) or the bread and wine merely symbolizing Christ's Body and Blood contradict Scripture.

Those who want to spiritualize away Christ's words should note that He said plainly, "This is ...," while referencing the physical elements. Similarly, St. Paul notes that those who receive the Lord's Supper in an unworthy manner are guilty of sinning against ... not the bread and wine, but against the Body and Blood of Christ.

As for John 6? Christ is speaking metaphorically, which makes sense in that context. Jesus is showing Himself to Israel as the fulfillment of God's salvation: Ancient Israel ate manna which, even though a miraculous gift of God, did not save anyone from sin, death, or the devil. Now, in their presence, was the true Manna, the true Bread from Heaven, Christ, Who would give Himself for the life of the world.

(By the way, actual "Sola Scriptura" people -- Lutherans -- refer to the Body and Blood of Christ actually being present in Communion as "Real Presence": In Communion, the Body and Blood of Christ are actually, physically present in, with, and under the bread and wine.)

Lutherans believe in Sola Scriptura, but they also believe in Real Presence (not transubstantiation). The big difference is between that and transubstantiation, there is no changing of the elements to the point that they also cease to be bread/wine. The Lutheran position is the elements become the true blood and body of Christ (both physically and spiritually known as "in, with, and under"), but they are also wine and bread. The reason behind this is the interpretation of scripture. There is nothing that explains how the wine and bread become the body and blood, nor is there mention of those elements ceasing to be elements. It's a divine mystery, yet the position is to take Christ at his word when he says it IS his body and IS his blood.

If they were just mere elements, then why is there such a warning of eating in an unworthy manner than can subject you to judgment?

We interpret them figuratively, not literally.

It's the same reason we don't believe God is literally a rock, a tower, or a shield, even though scripture describes Him in all those ways. Same reason we don't believe Jesus is literally a lamb, a lion, a hen, a piece of bread, a stone, a gate or door, or a vine. Same reason we don't believe that the new covenant is literally a cup, or that Peter is literally a rock or that Sarah and Hagar are literally two covenants.

These are all illustrations used to convey a point. Jesus did this all time when speaking in parables.

Matthew 13:34-35 ESV All these things Jesus said to the crowds in parables; indeed, he said nothing to them without a parable. This was to fulfill what was spoken by the prophet: “I will open my mouth in parables; I will utter what has been hidden since the foundation of the world.”

Most adherents of sola scriptura are memorialist in their understanding of the Eucharist. This means they believe Jesus was using a metaphor (albeit one God had intentionally set up beforehand). In the same way that the Scapegoat prefigured Christ*, or the Rock that Moses beat instead of struck prefigured Christ, so too the bread in the Passover prefigured Christ.

Transubstantiation, in the view of many Reformers, is the error of assuming Jesus was laying down dogma when he was merely using symbol. It is a common error even today.

To be painfully precise, the scapegoat ceremony consists of two goats. One, "the Lord's goat" took on the sins of the community and was sacrificed for it and prefigured Christ. His companion, who was loosed into the wilderness was technically the "scapegoat" and represents Satan. But nobody uses the expression "the Lord's goat," so I was going for the whole ceremony rather than the particular here. Kudos to @CRags for the keen eye.