That's not what it's saying. In John 10, Jesus divides christians into two groups: those who choose to obey His words and those who are not yet following in obedience. The ones that cannot be snatched away by any man are those who on their own free will chose to follow Him and walk in the light as He is in the light, (1 John 1:5-7). These are His sheep who He knows personally in a relationship, (John 14:21-23).
The second group of sheep (John 10:16) are christians also but are not yet following Christ in obedience. These can be easily lead astray and there's quite a few on CF in this category that has not come to know this.
John 10:27-29 is not about eternal security, it has absolutely nothing to do with it. It's all about a personal relationship, one based upon obedience in His word. John 14:21-23 is very explicit. You do His commandments, you will be loved by the Father and Son. Because they love you, they will come to live inside you as the holy spirit. This is the relationship and how it begins. That's what "My sheep hears my voice and I know them" means.
If you don't follow in obedience, there is not relationship. Christ will not come to live with willful sinners. Out of your own free will, you have to choose to follow Him first before He comes to you as the holy spirit. This is the second group of sheep that are currently lost, (John 10:16).
John 14:21-23
21 He who has My commandments and keeps them, it is he who loves Me. And he who loves Me will be loved by My Father, and I will love him and manifest Myself to him.”
22 Judas (not Iscariot) said to Him, “Lord, how is it that You will manifest Yourself to us, and not to the world?”
23 Jesus answered and said to him, “If anyone loves Me, he will keep My word; and My Father will love him, and We will come to him and make Our home with him.
In the bible, eternal life is not immortality, it's a personal relationship with God, (John 17:3).
John 3:15-16
15 That whosoever believeth in him should not perish, but have eternal life. (Relationship with God)
16 For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life. (Immortality)
Eternal life (relationship with God) is attain by following His commandments, (John 14:21-23, Matthew 19:16-21).
Matthew 19:16-22
16 And, behold, one came and said unto him, Good Master, what good thing shall I do, that I may have eternal life?
17 And he said unto him, Why callest thou me good? there is none good but one, that is, God: but if thou wilt enter into life, keep the commandments.
18 He saith unto him, Which? Jesus said, Thou shalt do no murder, Thou shalt not commit adultery, Thou shalt not steal, Thou shalt not bear false witness,
19 Honour thy father and thy mother: and, Thou shalt love thy neighbour as thyself.
20 The young man saith unto him, All these things have I kept from my youth up: what lack I yet?
21 Jesus said unto him, If thou wilt be perfect, go and sell that thou hast, and give to the poor, and thou shalt have treasure in heaven: and come and follow me.
Of course it's conditional, it's 110% conditional because it's all based on your free will.
You choose to follow Him, you are being saved. You choose to follow sin, you perish, (John 8:24, Luke 13:3, Romans 2:12, Matthew 5:30). You deny Him/His commandments, He will deny you, (2 Timothy 2:12, Matthew 10:33).
If you on your own free will choose to fall away that not even the holy spirit can convict you that you may be save, it's impossible for God to save you unless He takes away your free will and make you a robot. Then you no longer is a son or daughter of God.
God will not remove anyone's ability to decide on their own. You don't have to be perfect but if you don't make an effort to turn from sin, you end up in hell (whose end is to be burned). Christ's gift of salvation comes with a condition: keep my commandments, (John 14:21-23).
Hebrews 6:4-8
4 For it is impossible for those who were once enlightened, and have tasted of the heavenly gift, and were made partakers of the Holy Ghost,
5 And have tasted the good word of God, and the powers of the world to come,
6 If they shall fall away, to renew them again unto repentance; seeing they crucify to themselves the Son of God afresh, and put him to an open shame.
7 For the earth which drinketh in the rain that cometh oft upon it, and bringeth forth herbs meet for them by whom it is dressed, receiveth blessing from God:
8 But that which beareth thorns and briers is rejected, and is nigh unto cursing; whose end is to be burned.