"Such, I saw, have the carnal mind, therefore are not subject to the holy law of God. They are not agreed among themselves, yet labor hard with their inferences to wrest the Scriptures to make a breach in God's law, to change, abolish, or do anything with the fourth commandment rather than to observe it. They wish to silence the flock upon this question; therefore they get up something with the hope that it will quiet them and that many of their followers will search their Bibles so little that their leaders can easily make error appear like truth, and they receive it as such, not looking higher than their leaders. EW 69.1"
"Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be."
The EGW passage directly connects the 'carnal mind' with being 'not subject to the holy law of God,' mirroring the core idea of Romans 8:7. The connection is clear and intentional.
"I saw that those who oppose the Sabbath of the Lord could not take the Bible and show that our position is incorrect; therefore they would slander those who believe and teach the truth and would attack their characters. Many who were once conscientious and loved God and His Word have become so hardened by rejecting the light of truth that they do not hesitate to wickedly misrepresent and falsely accuse those who love the holy Sabbath, if by so doing they can injure the influence of those who fearlessly declare the truth. But these things will not hinder the work of God. In fact, this course pursued by those who hate the truth will be the very means of opening the eyes of some. Every jewel will be brought out and gathered, for the hand of the Lord is set to recover the remnant of His people, and He will accomplish the work gloriously. EW 69.3"
"Having a good conscience; that, whereas they speak evil of you, as of evildoers, they may be ashamed that falsely accuse your good conversation in Christ."
Both passages address the issue of false accusations and slander against believers. The EGW passage specifically mentions those who oppose the Sabbath, while 1 Peter 3:16 speaks more generally about those who speak evil of believers. The core idea of being falsely accused for one's faith connects them.