It's evident that religion can and has been used in politics from the values of voters and leaders. However, to use your religion or your relationship with God for making political decisions doesn't share the same meaning.
I've always loved finding all the best facts and research for argumentative work but I couldn't pursue that approach for this topic. Why? Because I've experienced the pattern in my relationship with God of how God defies logic.
God can't be contained to a definition or explanation. I liked the way I've heard one leader express that, "If you hear someone trying to explain to God as if he knows then he's a fool before he starts talking". That's a paradox within itself.
I've learned more recently to identify that the two sides of the paradox that you might wrestle with in understanding God are both true. That, yes, His hands are big and He knows exactly what to do to make you surrender but you'll also find no greater love than with Him because He has the biggest heart and knows what you need better than you do.
I think that accepting this paradox will differentiate between those that view politics religiously versus those that view it from 'what is God trying to do here'? The one that focuses on seeking 'what is God trying to do here?' would represent those with a relationship with God. This doesn't mean that referencing the laws of God exempts you from having a relationship but the love of God is the strength that sustains the relationship over the law. This is also a bit of a paradox because they're both important in Christianity.
There's the difference from seeing God as one-sided which is very prideful, limiting and incorrect compared to recognizing that His ways are higher than our ways and His thoughts are higher than our thoughts.
I believe that what we believe and how we see God will bring limitations or provision on how we can be used in God's plan for His kingdom on earth when it comes to the way the world is run.
God, our relationship with God and the law of God all have to be considered in the things we do as Christians.