“But they have not all obeyed the gospel. For Isaiah says, ‘Lord, who has believed what he has heard from us?'” (Rom 10:16).
"in flaming fire, inflicting vengeance on those who do not know God and on those who do not obey the gospel of our Lord Jesus." (2 Thessalonians 1:8)
1 Peter we are similarly told, “For it is time for judgment to begin at the household of God; and if it begins with us, what will be the outcome for those who do not obey the gospel of God?” (1Pe 4:17).
Given the context of these statements in the Bible, it likely along with that carries the richer meaning that the gospel is a royal summons to come under the lordship of Jesus Christ, to ally oneself with him, to follow him. It is the royal announcement that Jesus is the King who offers deliverance to all who, by the grace of God, fly to Him and he is the judge of those who would resist reign of God in Christ.
Wolfgang Musculus' a Reformed theologian of the Reformation had a commentary on 2 Thessalonians . This is his brief explanation of "obedience to the gospel" taken from his exposition of 1:8.
"And what is it to disobey the gospel of our Lord Jesus Christ? It is not simply to not hear, nor to not believe and acquiesce therein; but rather it is to be unwilling to hear, to believe and to rest therein; and indeed to rather set oneself in opposition to it. One the other hand, to obey the gospel is to dedicate yourself to the Lord Christ with your whole heart - to hearing, believing, trusting and obeying him as your only Lord and Savior. He obeys his doctor who believes his words and happily receives the treatment which he provides, adhering to his instruction in all things. In doing this, he not only brings glory to the doctor, but also receives health for himself; likewise, he who obeys the gospel of our Lord Jesus Christ believes his testimony, and eagerly receives the grace given to him, while also resting obediently in his precepts. And he who does this glorifies Christ, and also wisely looks to his own salvation purchased for him by the blood of Christ."
Of course obedience to the gospel can only be done with renewal of heart. God commands us (the church) to declare the summons to believe the gospel of Jesus Christ. It would be futile if it only depended on the people hearing the summons because their ears are willfully closed to it, but God has us proclaim it anyway because this is his chosen method for gathering His elect since He is the one who can open ears and disarm the hostility of man's heart to the gospel.