There is noting "conditional" about what the Lord Jesus says here:
"All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out" (Jn.6:37).
According to your mistaken view the Lord Jesus will indeed cast out some who come to Him, because He will cast out those who do not continue to follow Him:
Those with saving faith know that they will always follow the Lord, no matter what! If you do not know that you will always follow Him then your faith will not serve to save you.
You think Paul and others were wasting their breath in saying--
1Co 10:1 Moreover, brethren, I would not that ye should be ignorant, how that all our fathers were under the cloud, and all passed through the sea;
1Co 10:2 And were all baptized unto Moses in the cloud and in the sea;
1Co 10:3 And did all eat the same spiritual meat;
1Co 10:4 And did all drink the same spiritual drink: for they drank of that spiritual Rock that followed them: and that Rock was Christ.
1Co 10:5 But with many of them God was not well pleased: for they were overthrown in the wilderness.
1Co 10:6 Now these things were our examples, to the intent we should not lust after evil things, as they also lusted.
1Co 10:7 Neither be ye idolaters, as were some of them; as it is written, The people sat down to eat and drink, and rose up to play.
1Co 10:8 Neither let us commit fornication, as some of them committed, and fell in one day three and twenty thousand.
1Co 10:9 Neither let us tempt Christ, as some of them also tempted, and were destroyed of serpents.
1Co 10:10 Neither murmur ye, as some of them also murmured, and were destroyed of the destroyer.
1Co 10:11 Now all these things happened unto them for ensamples: and they are written for our admonition, upon whom the ends of the world are come.
1Co 10:12 Wherefore let him that thinketh he standeth take heed lest he fall.
2Pe 2:18 For when they speak great swelling words of vanity, they allure through the lusts of the flesh, through much wantonness, those that were clean escaped from them who live in error.
2Pe 2:19 While they promise them liberty, they themselves are the servants of corruption: for of whom a man is overcome, of the same is he brought in bondage.
2Pe 2:20 For if after they have escaped the pollutions of the world through the knowledge of the Lord and Saviour Jesus Christ, they are again entangled therein, and overcome, the latter end is worse with them than the beginning.
2Pe 2:21 For it had been better for them not to have known the way of righteousness, than, after they have known it, to turn from the holy commandment delivered unto them.
2Pe 2:22 But it is happened unto them according to the true proverb, The dog is turned to his own vomit again; and the sow that was washed to her wallowing in the mire.
Heb 3:6 But Christ as a son over his own house; whose house are we, if we hold fast the confidence and the rejoicing of the hope firm unto the end.
Heb 3:7 Wherefore (as the Holy Ghost saith, To day if ye will hear his voice,
Heb 3:8 Harden not your hearts, as in the provocation, in the day of temptation in the wilderness:
Heb 3:9 When your fathers tempted me, proved me, and saw my works forty years.
Heb 3:10 Wherefore I was grieved with that generation, and said, They do alway err in their heart; and they have not known my ways.
Heb 3:11 So I sware in my wrath, They shall not enter into my rest.)
Heb 3:12 Take heed, brethren, lest there be in any of you an evil heart of unbelief, in departing from the living God.
Heb 3:13 But exhort one another daily, while it is called To day; lest any of you be hardened through the deceitfulness of sin.
Heb 3:14 For we are made partakers of Christ, if we hold the beginning of our confidence stedfast unto the end;
LA