Some Christian associations request government protection for safety reasons. As biblical Christians, can we take or pursue government protection?

Short answer:  Yes, Christians may use legal means to secure safety.

Explanation:  The Apostle Paul asked for and received Roman government protection when the Jews were enraged by him.  Acts 23:10-24 (NIRV), “The arguing got out of hand. The commanding officer was afraid that Paul would be torn to pieces by those who were arguing. So he ordered the soldiers to go down and take him away from them by force. They were supposed to bring him into the fort.

“The next night the Lord stood near Paul. He said, ‘Be brave! You have given witness about me in Jerusalem. You must do the same in Rome.’ 

“The next morning the Jews gathered secretly to make plans against Paul. They took an oath that they would not eat or drink anything until they had killed him. More than 40 men took part in this plan. They went to the chief priests and the elders. They said, ‘We have taken a strong oath. We have made a special promise to God. We will not eat anything until we have killed Paul. Now then, you and the Sanhedrin must make an appeal to the commanding officer. Ask him to bring Paul to you. Pretend you want more facts about his case. We are ready to kill him before he gets here.’

“But Paul's nephew heard about this plan. So he went into the fort and told Paul. Then Paul called one of the commanders. He said to him, ‘Take this young man to the commanding officer…What do you want to tell me?’ the officer asked. He said, ‘The Jews have agreed to ask you to bring Paul to the Sanhedrin tomorrow. They will pretend they want more facts about him. Don't give in to them. More than 40 of them are waiting in hiding to attack him. They have taken an oath that they will not eat or drink anything until they have killed him. They are ready now. All they need is for you to bring Paul to the Sanhedrin.’ The commanding officer let the young man go. But he gave him a warning. ‘Don't tell anyone you have reported this to me,’ he said.

“Then the commanding officer called for two of his commanders. He ordered them, ‘Gather a company of 200 soldiers, 70 horsemen and 200 men armed with spears. Get them ready to go to Caesarea at nine o'clock tonight. Provide horses for Paul so that he may be taken safely to Governor Felix.’”

God had told Paul that he was to go to Rome to spread the Gospel. The Apostle Paul conformed his actions to God’s will and asked for Roman protection to safeguard himself from a Jewish mob. Thus, God used Roman soldiers and horsemen to protect Paul so that he might arrive safely at Rome.