What are some biblical truths that aren't Christian?

God's word is truth so it's biblical truths taken and distorted by others that we need to beware of. Claims that seem to be the same but which have subtle differences are the most likely to deceive. This R&S site is awash with them. But all biblical truth is  Christian. It's the interpretation of them that causes all the confusion. Then people end up arguing about words, which the Bible warns Christians not to do - 1 Timothy 6:4. Many want to justify themselves, to prove themselves right. Pity help them on the Day of Judgment.

What the churches use to preach young men into their endless wars.  Some churches teaches hate for others.  So those things are not Christian.  www.jw.org to find the truth.

Your take on Scripture has some flaws, but no matter...

There are some biblical truths that even many Christians do not accept as true. 

For example, Jesus came and took away the sins of the world.  But many Christian churches are still hung up on sin and its avoidance. There is but one sin that can condemn a person now; and it is not a sin of commission or omission. It is the sin of unbelief; a sin of the mind and thought.

Regarding your take on things;

The bible reveals the nature of the soul (AKA the unseen) as eternal, and eternal means no beginning and no end, meaning we existed before we came here, which paired with the constant theme of birth, death and rebirth should tell you something.

The Bible states that souls are created. Adam "became" a living soul. "Eternal" needs to be understood in context as well as the word or words in Hebrew and Greek that are translated as such, by studying the etymology of those words and how they were used when those parts of the Bible was written.

Many truths existed in Judaism long before Jesus Christ was born. When He founded His Church, He included those truths that were previously known in Judaism, and revealed many additional truths to the one Church He founded. Therefore, all Christian truths are taught by the original and true Christian Church, the one Church Jesus founded, which He said was to remain one, but some of those truths originated in Judaism.

God is a tangible being of flesh and bones who created Adam specifically in his own image and likeness, not borrowed or assumed ones.  So is Jesus Christ.  (The Trinity is a heresy that is unsupported in the Bible except for the forged Johannine Comma.)  Jesus Christ is Jehovah incarnate, the creation and begotten son of God.

Our spirits really are the children of God.

The resurrections are tangible, physical, and immortal.

Jesus shall reward us according to our works, not our beliefs, much less some nebulous "acceptance" or some arbitrary whim of God's.

Repentance is more than saying "sorry" to God.  We actually have to regret the behavior, give it up forever, and make what amends we can that won't make matters worse.

Every single one of God's human children, past, present, and future, shall have a fair chance to learn the gospel of Christ (1 Peter 3:18-20; 4:6) and benefit from it (1 Cor. 15:29)

For a more detailed analysis of what the Bible and other early Christian sources say, read "To the Law and To the Testimony."

"God helps them who help themselves." This old adage is not only not Christian, but it's not true!

As for each and every one of you statements, they are all false statements, and lies. There is a morsel of truth in each one, but when examined more closely, all are lies, and unbiblical at their core. For example: Not judging others' walks with God?  You will find that statement at the beginning of Matthew 7, but the following few verses direct us to not use a double standard when we do judge. Indeed, the entirety of Matthew 7 is about discerning and judging other righteously, for the sake of the believer's walk with the Lord. 

Simple, biblical truth consists of the word of God, described in holy scripture. Anyone who does not observe the whole word of God, but distorts it, is out of Christian doctrine.

John 14: 23-24.

Jesus answered 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. 24 Whoever does not love me does not keep my words; the word that you hear is not mine, but the Father's who sent me.

(Ezekiel 18:4) Look! All the souls—to me they belong. As the soul of the father so also the soul of the son—to me they belong. The soul who sins is the one who will die.

- The Bible never says that abortion is a sin. 

- The Bible says only faith can get a person to Heaven. It also says works are the most important undertaking for a person to get to Heaven. One of them is wrong.

- Bible never says that suicide is a sin.

- Bible refers to Hell even though the concept of Hell wasn't created until the 3rd century by Augustine.

The "Golden Rule", do unto others...was taught by Buddha 500 years before Jesus was born.

The "7 Deadly Sins" are NOT in the Bible, but many people think these are sins.  They were written by a monk many years later.

You can read more here: 

https://en.wikipedia.org/wiki/Seven_deadly_sins