Knowing God exists is beyond empirical evidence. Two people, one a believer and the other an atheist, can assemble equally valid arguments to prove their perspective, but each must make a leap of faith to their respective beliefs. I know this because I've had such conversations.  
Considering this and speaking from a perspective of faith, it makes sense to me that I live to reveal God as I understand God--as gracious, loving, merciful, just, holy. What does it say about God if I behave in ways that diminish others because of who they are or how they live; or if I do not live as if creation itself is a work of God's hands? I might as well enter the Louvre with a hammer and blowtorch and begin destroying the priceless art of masters. This attitude of generosity must apply to all for it to be worthy of representing God--therefore it must extend even to those who disagree with me and represent the antithesis of my beliefs.
The way I live in the world and treat others is a far greater statement of my theology than volumes of systematic doctrine or biblical commentary (or bumper stickers or posts on social media sites)