"For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuse" (Romans 1:20).

The Bible is a revelation given by God of Himself, a theology.  Since worship is the most definitive feature of every human life, it is critical that we receive this revelation and honour God accordingly.  Otherwise, we are worshipping another god. That is idolatry.

The very first theological truth revealed (in the opening chapters of Genesis) is that God is the Creator of all things.  This is foundational to all the Bible teaches concerning man's relationship to God.  However, because men tend to believe what they wish were true rather than what is, there has been widespread acceptance of the theory of origins known as evolution.
Romans 1:20 exposes the intellectual dishonesty of embracing a belief which denies a Maker while living in the midst of "the things which are made".  Man's very constitution as a rational creature means he understands and sees clearly something of the wisdom and power of the one who made the universe.  The previous verse tells us that "God hath showed it unto them".
In fact, pure secular evolutionary dogma is so unsatisfying to the human perception that it is gradually morphing into a religious variant that makes god everything and everything god - kind of self creating.  The astute observer will immediately recognize this as nothing but pantheism.  So evolutionary doctrine has served to deny the God of the Bible, and now opens the door for the reemerging of the ancient Pagan concept of god(s) into Western thought.
Today, under the name of New Age teaching, even professing Christianity is being moved away from the theology and God of the Bible.  This concept makes everyone god, or part of god.  It distorts the truth historically recognized by Christians that there is a fundamental difference between Creator and creature.  It distorts the large body of Bible teaching to do with our accountability to God, and questions the seriousness of sinning against His holy laws.
Saddest of all, for those deceived by it, denial of God's place as Creator also denies the need of salvation through His Son by His sacrifice on the cross.  The Christianity of the Bible cannot be mixed with atheistic teachings without eternal loss.
"But we are sure that the judgment of God is according to truth against them which commit such things" (Romans 2:2).

Romans teaches us the theological fact that God is a God of truth.  This is seen here in His judgment.  The courts and tribunals of this world are often heavily influenced by the knowledge of who the accused is.  Lady Justice frequently lifts the blindfold and peeks before rendering a decision.  However, God is concerned only with the truth.  "For there is no respect of persons with God" (Romans 2:11).

God is absolutely true in everything He says.  He has commanded us not to lie because that is His own standard.  Because He is God, He simply cannot lie.  "In hope of eternal life, which God, that cannot lie, promised before the world began" (Titus 1:2).  This means that His written word is also completely trustworthy.  It is truth itself.  "Sanctify them through thy truth: thy word is truth" (John 17:17).
There is a great contest for the minds and confidence of the men of this world.  The world is full of lies about everything moral, spiritual, and eternal.  Yet the Bible speaks with absolute veracity and trustworthiness on those same things.  Jesus told people in chapter eight of John that Satan is the father of lies, and the hearts of men incline to those ways naturally.  People don't disbelieve the Bible because it is untrue, but because it is true.  "And because I tell you the truth, ye believe me not" (John 8:45).
The truth sometimes hurts.  The Bible offers a way of salvation that can only be received as part of a message of truth.  Jesus Christ, God's Only Begotten Son, paid for our sins by dying a horrible death.  Because the punishment fits the crime, the Gospel story not only tells of a free salvation, it tells of a great guilt of sin on our part.
You can't trust Christ for forgiveness of sin without coming face to face with truth.  Jesus is the way of salvation and is Truth itself.  "Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me" (John 14:6).  Churches and pulpits need to stop looking for crowd pleasing messages to achieve success and return to teaching and preaching Bible truth for the good of their hearers.
"Is God unrighteous who taketh vengeance? (I speak as a man) God forbid: for then how shall God judge the world?" (Romans 3:5b-6).

Paul is here defending his teaching about mankind's sinfulness and guilt before God.  He has adopted the role of a prosecuting attorney to prove that everyone has broken God's law and is in need of forgiveness.  Knowing human nature, he has anticipated objections and now is going on to prove that the particular objection in view is invalid.

In effect, his point here is that judgement of the world by God is a basic axiom, a first principle of theology.  Therefore any idea or argument that would deny Him the right to judge men can simply be rejected out of hand.  We may not dismantle God by taking away the fundamental attributes that make God to be God.  God will judge the world.  Period
But it is common to this day for people to live by philosophies and standards that rest upon the very notion that they will never face God's judgement.  But God will not cease to be God or to exercise His divine prerogatives.  It is the sinner that must change to escape a disaster that is beyond words to express, falling under the wrath of Almighty God at Judgement Day.
God is scrutinizing the lives and hearts of you and me right now.  "The LORD is in his holy temple, the LORD'S throne is in heaven: his eyes behold, his eyelids try, the children of men" (Psalm 11:4).  That's watching and measuring us pretty carefully.  The consequence is sober indeed.  "Upon the wicked he shall rain snares, fire and brimstone, and an horrible tempest" (Psalm 11:6a).
But none of this is revealed to us to bring us to despair.  It is far better to know our danger now, so we can do something about it.  The next thing for us after death is the judgement.  It is better to deal with the problem now while we may than to think of it with terrible regrets for ever in hell.  No matter how busy we are or how frightening the topic seems to us.
When Jesus Christ, God's Son died on the cross, He already suffered the penalty for our sins.  Now risen from the dead, He invites us to turn from our sins and receive Him personally as Lord and Saviour.