They didn't apply their knowledge since "they did not honor Him as God, or give thanks" (Ro 1:21). It was a deliberate decision because "they did not see fit to acknowledge God" (:28). They "suppress the truth" (:18). They "exchanged the glory" (:23) and "the truth of God for a lie" (:25). In their pride they claimed "to be wise" (:22) and "worshipped and served the creature rather than the Creator" (:25). By their behavior they sealed their own fate. When they "became futile in their speculations" (:21) it gave "birth to sin . . . [which] brings forth death (Jas 1:15). Therefore God "gave them over" (Ro 1:24, 26, 28) to the desires of their hearts. "Their foolish heart was darkened" (:21) in the form of "impurity" (:24) and "degrading passions" (:26) which are acts of sexual indecency. They received "in their own persons the due penalty of their error" (:27). Finally "God gave them over to a depraved mind" (:28) and worse things happened.
What do you think the destiny of those who "suppress the truth in unrighteousness" (Ro 1:18), "exchanged the truth of God for a lie" (:25), and "do not obey the truth, but obey unrighteousness" (2:8) will be? There will be "wrath and indignation . . . tribulation and distress for every soul of man who does evil" (:8-9). You take the wrong direction when you don't "honor Him as God or give thanks" (1:21). When you claim "to be wise" (:22) yourself and do "not see fit to acknowledge God any longer" (:28) you become "selfishly ambitious" (2:8). You serve instead "the creature rather than the Creator" (1:25) and your "heart was darkened" (:21). "You are storing up wrath for yourself in the day of . . . the righteous judgment of God" (2:5). Your "end will be according to their deeds" (2Co 11:15). But if you go the right direction there will be "glory and honor and peace to everyone who does good" (Ro 2:10). If you don't "hold fast . . . until the end" (Heb 3: 6) then you won't be saved.
Having the truth is crucial since "they perish because they refused to love the truth and so be saved" (2Th 2:10). They "suppress the truth by their wickedness" (Ro 1:18). The knowledge of God was accessible but people closed their minds to it. "They did not think it worthwhile to retain the knowledge of God" (:28). The truth of God has been "clearly seen . . . [and] men are without excuse" (:20). It is a matter of what one decides in his mind. "Their thinking became futile and their foolish hearts were darkened" (:21). They didn't glorify God or give thanks (:21) and then "claimed to be wise" (:22). "God sent them a powerful delusion so that they will believe the lie and so be condemned who have not believed the truth but have delighted in wickedness" (2Th 2:11). "Because of this, God gave them over to shameful lusts" (Ro 1:26). God had protected them before. But "since they did not think it worthwhile to retain the knowledge of God, he gave them over [again] to a depraved mind" (:28). "As a man thinks in his heart, so is he" (Pr 23:7).