God gave them over to a REPROBATE mind

[TonyChanYT]

King James Bible, Romans 1:

28 And even as they did not [οὐκ] like to retain [G1381] God in their knowledge, God gave them over to a reprobate [G96] mind, to do those things which are not convenient;

Let's check another Greek word δόκιμος [G1384] which is not in the verse. Thayer's Greek Lexicon for G1384:

properly accepted, particularly of coins and metals

Studylight:

In the ancient world there was no banking system as we know it today, and no paper money. All money was made from metal, heated until liquid, poured into moulds and allowed to cool. When the coins were cooled, it was necessary to smooth off the uneven edges. The coins were comparatively soft and of course many people shaved them closely. In one century, more than eighty laws were passed in Athens, to stop the practice of shaving down the coins then in circulation. But some money changers were men of integrity, who would accept no counterfeit money. They were men of honour who put only genuine full weighted money into circulation. Such men were called "dokimos" or "approved". Donald Barnhouse

The word means "approved" like approving the coin had not been shaved. It had its full weight.

G1381 (δοκιμάζω) is the first keyword in the verse. It is actually the verb form of the adjective G1384-properly-approved.

The second keyword in the verse is G96-reprobate which is made of the prefix ἀ and the headword δόκιμος [G1384]. G96 is an adjective. Thayer's Greek Lexicon:

not standing the test, not approved; properly of metals and coin

Literal Standard Version:

And according as they did not approve of having God in knowledge, God gave them up to a disapproved mind, to do the things not seemly;

Basically, these so-called reprobates were like counterfeit money. They did not approve of God, so God did not approve of them.

G96 also appears in Hebrews 6:

8 But land that produces thorns and thistles is worthless [G96] and is in danger of being cursed. In the end it will be burned.

Young's Literal Translation:

and that which is bearing thorns and briers is disapproved of [G96], and nigh to cursing, whose end is for burning;

G96 does not necessitate that the person will 100% go to hell but if he does not change, he would. He is a counterfeit. He does not carry the full weight. He is not a reprobate in the Calvinist sense, i.e., a sinner who is not of the elect and is predestined to damnation.

Even the New King James Version changed its wording:

And even as they did not like to retain God in their knowledge, God gave them over to a debased mind, to do those things which are not fitting.

See also Was it possible for Paul to become a G96-REPROBATE?.