Should Christians Be Involved in Government and Social Issues?

YES. THERE ARE TANGIBLE BENEFITS AND IT’S BIBLICAL:
GOVERNMENT ORDAINED BY GOD

Romans 13:1-4 Let every person be subject to the governing authorities. For there is no authority except from God, and those that exist have been instituted by God.

Colossians 1:16-20 …God created everything in heaven and earth. He made the things we can see and the things we can’t see—kings, kingdoms, rulers, and authorities.

Daniel 2:21 …He removes kings and sets up kings; He gives wisdom to the wise and knowledge to those who have understanding;
 
SCRIPTURE COMMANDS BELIEVERS TO BE INVOLVED IN SELECTING GOVERNING AUTHORITIES

Exodus 18-21 …choose able men from all the people, such as fear God, men who are trustworthy and who hate a bribe; and place such men over the people as rulers…
 
GOVERNMENT IMPACTS DAILY LIFE; BELIEVERS ARE URGED TO PRAY FOR ELECTED OFFICIALS

1 Timothy 2:1-4 First of all, then, I urge that supplications, prayers, intercessions, and thanksgiving be made for all men, for kings and all who are in high positions, that we may lead a quiet and peaceable life, godly and respectful in every way.

Acts 1:14 All continued with one accord in prayer.
"In prayer the Church has received power to rule the world …if it would stay together on its knees, it would dominate world politics - from the prayer room." O. Hallesby
 
GOD WARNS THAT THERE ARE CONSEQUENCES FOR LACK OF PARTICIPATION IN THE GOVERNMENTAL PROCESS

Proverbs 29:2 When the righteous are in authority, the people rejoice; but when the wicked rule, the people groan.
 
GOD WARNS THAT THERE ARE CONSEQUENCES WHEN BELIEVERS DO NOT ACT ON BIBLICAL PRINCIPLES

Matthew 5:13 You are the salt of the earth. But what good is salt if it has lost its flavor? Can you make it useful again? It will be thrown out and trampled underfoot as worthless.

James. 4:17 Remember, it is sin to know what you ought to do and then not do it.
 
GOD PROMISES BLESSINGS WHEN BELIEVERS PRAY

II Chronicles 7:14 …if my people who are called by my name humble themselves, and pray and seek my face, and turn from their wicked ways, then I will hear from heaven, and will forgive their sins and heal their land.