As for Christians getting involved in politics...if only more Christians, real Christians, were! We are supposed to be salt and light, and we are supposed to use whatever gifts God gave us. If more of us were in government, the British Parliament would not even be having the current Gay Marriage Bill; it would never have arisen. The whole gay rights issue would have been booted right out from the start, along with whoever raised it.
We only got rid of child labour, slavery, cruelty of all sorts because there were Christians, here and in America, standing up for Bible values. God has raised up men in both countries to stand for Him through the centuries, but now the tide of evil is so great that they are sidelined. If Wilberforce had not stood up, we might still have slavery. If Christians had not started Sunday Schools (the 'ragged schools'), there might not be any schools today, and ordinary people might never have learned to read and write.
History is coming to a head now. The wheat and the tares are growing together, and things like the horrible Gay Marriage Bill are the flowering of the tares. We know from Bible prophecy that it can't be long now before the Lord puts a stop to all this. The Great Tribulation will take care of it. Then, in the Millennium*, we will certainly be involved, though the 'politics' will be a whole lot simpler - King Jesus will rule from Jerusalem, and we will joyfully carry out His wishes, as administrators, judges, teachers - whatever role He assigns for each of us. For the rebellious, there will be the rod of iron.
And for now, it is wise not to get all worked up, since there is not much we can do. After all, 'Evil men and seducers shall wax worse and worse, deceiving and being deceived.' 2 Tim 3:13
But although we don't get too worked up, who can help but grieve for our countries? Even there, the Lord gives us such a precious promise: 'Blessed are they that mourn, for they shall be comforted.' Matthew 5:4.
And here's another good scripture: 'Thou will keep in perfect peace he whose mind is stayed on Thee, because he trusts in Thee.' Isaiah 26:3
What a God we serve; what a Book He gave us!
*The Millennium is the 1,000 year reign of Christ, which will follow the seven year Great Tribulation. Most churches never teach on this, and many leaders of churches do not believe in it, although the Bible repeats it six times in the Book of Revelation, Chapter 20. This is all in our books, plus a lot more.