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Note that this doesn't apply to all groups that adhere to Sola Fide. Plenty of groups believe that we have no part in our own salvation, even in choosing to believe, but this is one perspective that's relatively common among Evangelicals.
Short version:
These verses are simply Jesus teaching on the true definition of what God's standard for "good" is.
Longer version:
These verses are very similar to those in Matthew 5, where Jesus explains that lust is the same as adultery, hatred the same as murder, etc. Jesus was dealing with the Jewish people, who were under the impression that their obedience to the Law would save them. By teaching them the Truth of just how high God's perfect standard is, He was preparing them to understand that they are not truly "good" at all.
Any reasonable person would hear those words and think "there's no way I can be that good and perfect. I'm doomed". To those that hold this view, that's the necessary realization of one's sinful nature that's necessary to drive us to repentance.
An example of one such ministry that holds this view would be Living Waters/The Way of the Master, headed by Ray comfort and Kirk Cameron. Example: Am I good enough to go to Heaven?
Expanding a bit on the necessity of realizing our sinful nature to drive us to repentance, Ray Comfort says this in his Hell's best kept Secret teaching... (This is a paraphrase from memory, but it's close)
You try to save a man from drowning when he doesn't think he is. Jump in, pull him to the shore without telling him anything, he's not going to be too happy with you. But if he sees that he is drowning, he will be grateful, and won't despise the gift.
These verses show that God's standard is perfect, and that we fall short. This is perfectly in harmony with the idea of salvation by faith alone apart from works. God's Law can't save us. it can only show us ourselves in our true nature, so that we can see the need to be saved.
From Bible Study Planet:
Once a person has understood the Law, and its spiritual meaning and content, he knows that can’t keep it. What’s the summary of the Law? It is: “You shall love the Lord thy God with all your heart, and all your soul, and all your mind, and all your strength; and you shall love you neighbor as yourself.” (Luke 10:27)
Paul also wrote of this extensively in the Book of Romans. Two small excerpts:
Now we know that whatever the law says, it says to those who are under the law, so that every mouth may be silenced and the whole world held accountable to God. Therefore no one will be declared righteous in his sight by observing the law; rather, through the law we become conscious of sin. (Romans 3:19-20)
...
What shall we say then? Is the Law sin? May it never be! On the contrary, I would not have come to know sin except through the Law; for I would not have known about coveting if the Law had not said, "YOU SHALL NOT COVET." (Romans 7:7)
Upvote:5
The gospel never promises anyone with fake faith salvation. Rather it uses both encouragements and warnings as a means to preserve all the elect into everlasting eternity.
This sort of question can be asked from many verses in the Bible because it rests upon a sometimes-unconscious assumption that ‘God would never warn someone of something, that according to his foreknowledge would never happen.’ This is simply not true. One reason why God knows that something will never happen is because he effectively ensures it does not – partly through his warning that it could.
So the basic meaning of this verse, using bold imagery, is a sin like adultery, for example, should be despised at the utmost. Extending this imagery to its furthers extent, in principle if it came between having our eye, verses having women, we should depart with our eyes happily! In a less symbolic way, if we have the choice of sin and the world, or Christ and our own death, the principle of wisdom and spiritual survival would be to choose Christ. This is the beginning of the gospel. Which goes ‘repent and believe’.
The gospel goes further, ‘repent and believe the good news’! One of the most precious things a sinner will not give up is his own righteousness. In fact this may be the most common idol men will not let go. Extending this sermon further to rank unbelief and self-righteousness we can easily extend the application by saying: ‘If a man prefers self-righteousness to God’s free gift, then he is like a man that refuses to cut away his valued possession (eye). For that he can be certain that he will spend eternity in hell as a just reward for rejecting the gospel. This is not a subject for playing eternal games with God and our own soul!