Carey and the others wrote:
As we consider it our duty to honour the civil magistrate, and in every state and country to render him the readiest obedience, whether we be persecuted or protected, it becomes us to instruct our native brethren in the same principles. A sense of gratitude too presses this obligation upon us in a peculiar manner in return for the liberal protection we have experienced. It is equally our wisdom and our duty also to show to the civil power, that it has nothing to fear from the progress of Missions, since a real follower of Christ must resist the example of his great Master, and all the precepts the Bible contains on this subject before he can become disloyal. Converted heathens, being brought over to the religion of their Christian Governors, if duly instructed, are much more likely to love them, and be united to them, than subjects of a different religion.

Modern English Version of that:
As we see it as our duty to honour civil authorities and to obey them readily in every state and country – whether we are being persecuted or protected – we should also teach our fellow countrymen the same values. We feel a special obligation to do this out of gratitude for the generous protection we have received.
It is both wise and our responsibility to show civil authorities that they have nothing to fear from the growth of missions. A true follower of Christ would have to go against the teachings of Jesus and the Bible to be disloyal. When non-Christians embrace the faith of their Christian leaders and are properly educated, they are much more likely to love and unite with them than those who follow a different religion.

Related Scriptures:
1 Cor 2:2
“For I decided to know nothing among you except Jesus Christ and Him crucified.”
Romans 13:1-2
“Let everyone be subject to the governing authorities, for there is no authority except that which God has established. The authorities that exist have been established by God. Consequently, whoever rebels against the authority is rebelling against what God has instituted, and those who do so will bring judgment on themselves.”
1 Peter 2:13-17
“Submit yourselves for the Lord’s sake to every human authority: whether to the emperor, as the supreme authority, or to governors, who are sent by him to punish those who do wrong and to commend those who do right. For it is God’s will that by doing good you should silence the ignorant talk of foolish people. Live as free people, but do not use your freedom as a cover-up for evil; live as God’s slaves. Show proper respect to everyone, love the family of believers, fear God, honour the emperor.”
Matthew 22:17-21
“Tell us then, what is your opinion? Is it right to pay the imperial tax to Caesar or not? But Jesus, knowing their evil intent, said, ‘You hypocrites, why are you trying to trap me? Show me the coin used for paying the tax.’ They brought him a denarius, and he asked them, ‘Whose image is this? And whose inscription?’ ‘Caesar’s,’ they replied. Then he said to them, ‘So give back to Caesar what is Caesar’s, and to God what is God’s.'”
Titus 3:1
“Remind the people to be subject to rulers and authorities, to be obedient, to be ready to do whatever is good.”
Acts 5:29
“Peter and the other apostles replied: ‘We must obey God rather than human beings!'”