You're stating that man knows God exists, Romans 1 does teach that it is his eternal power and divine nature that have been revealed through "Natural or General Revelation". However, if you read further in Romans 1 from Romans 1:21 and further, your argument is lost. Especially if you consider into the further chapters. Romans chapter 3:
Rom 3:10 as it is written: "None is righteous, no, not one;
Rom 3:11 no one understands; no one seeks for God.
Rom 3:12 All have turned aside; together they have become worthless; no one does good, not even one."
You clearly ignore what you want and bend Scripture in order to fit your own contrived doctrine.
Romans 1:21 is an example of judicial hardening and giving man up to his own desires and allowing him to become totally depraved through continued hardening of his hard against the truth of God that he knows but trades for a lie as a just judgment against him (Romans 1:18, 25). Look how your text does not support you:
Rom 1:21 Because,
knowing God, they did not glorify Him as God, neither were thankful. But they
became vain in their imaginations, and [as consequence] foolish heart was darkened.
And if read even further to the end of the chapter your case further falls apart:
Rom 1:26
For this cause, God
gave them up to dishonorable affections. For even their women changed the natural use into that which is against nature.
Rom 1:27 And likewise also the men, leaving the natural use of the woman, burned in their lust toward one another; males with males working out shamefulness, and receiving in themselves the recompense which was fitting for their error.
Rom 1:28 And even as they did not think fit to have God in their knowledge, God gave them over to a reprobate mind, to do the things not right,
Rom 1:29 being filled with all unrighteousness, fornication, wickedness, covetousness, maliciousness; being full of envy, murder, quarrels, deceit, evil habits, becoming whisperers,
Rom 1:30 backbiters, haters of God, insolent, proud, braggarts, inventors of evil things, disobedient to parents,
Rom 1:31 undiscerning, perfidious, without natural affection, unforgiving, unmerciful;
Rom 1:32 who,
knowing the righteous order of God, that those practicing such things are worthy of death, not only do them, but have pleasure in those practicing them.
If you go back to the original Psalms Paul is quoting in your Romans 3 proof text you will see how it contradicts you:
Psa 14:1 To the chief Musician, A Psalm of David. The fool hath said in his heart, There is no God.
They [the fools that say in their heart there is no God, or the Hebrew could be translated as "no God" meaning they say no to God] are corrupt, they have done abominable works, there is none that doeth good.
Psa 14:2 The LORD looked down from heaven upon the
children of men [mere children of man not children of God; doesn't refer to every single last human that has existed, exists or will exist, we generalizations like this all over Scripture, examples: Col 1:23 if indeed you continue in the faith grounded and settled, and are not moved away from the hope of the gospel, which you have heard and which was proclaimed in all the creation under Heaven, of which I, Paul, became a minister,; Mar 16:15 And he said unto them, Go ye into all the world, and preach the gospel to every creature. . . . Mar 16:20 And they went forth, and preached every where, the Lord working with them, and confirming the word with signs following. Amen.], to see if there were any that did understand, and seek God.
Psa 14:3 They are all gone aside, they are all together become filthy: there is none that doeth good, no, not one.
Psa 14:4 Have all the
workers of iniquity no knowledge? who eat up
my people as they eat bread, and call not upon the LORD.
[see the distinction between "workers of iniquity" vs. "my people"?]
Psa 14:5 There were they in great fear:
for God is in the generation of the righteous.
[O so there is some who are righteous and that is who God is with. Thus we see a distinction between these people and those of whom there is none righteous no not one.]
Psa 14:6 Ye have shamed the counsel of the poor, because the LORD is his refuge.
Psa 14:7 Oh that the salvation of Israel were come out of Zion! when the LORD bringeth back the captivity of his people, Jacob shall rejoice, and Israel shall be glad.
Now knowing this but ignoring it and just taking this proof text of your for the sake of argument:
Rom 3:10 as it is written: "None is righteous, no, not one;
[does this say, no one is able to be righteous, no not one?]
Rom 3:11 no one understands; no one seeks for God.
[does this say, no one is able to understand, no one is able to seek after God?]
Rom 3:12 All have turned aside; together they have become worthless; no one does good, not even one."
[does this say, people have no choice but to turn aside, have no choice but to become worthless, have no ability to do good, not even one?]
Using Romans is very bad to teach what you do by isolating it. All throughout in context one of the main themes is that salvation is not only for Jews but also for Gentiles. It is written against Jews who say only Jews who have received the Law can be saved and is written to refute this and show this is a lie. Paul argues that both Jews and the nations are under sin (Rom. 3:9), and so both need a savior, and because God is not an unjust respecter of persons (Rom. 2:11 ), salvation in Christ is for all peoples. All peoples have sinned and fallen short of God's glory and so all peoples need salvation in Christ and so God who shows no favoritism offers it to all peoples not just Israel. That is the point of Romans, sir.
"You clearly ignore what you want and bend Scripture in order to fit your own contrived doctrine."
Really? Because that is how I see you.