What are your thoughts about this kind of religious/political clash?
Saying "Don't pray. Take action." is like saying don't train before you go to war, just go to war. Or don't continue training during the war, just point and shoot mate.
To the Christian, acting without prayer is equivalent to acting with no preparation before hand or refinement after hand. Such action is completely from instinct. It is a self-centered, narrow-sighted whim.
However, prayer that does not lead to action is arguably not prayer; one begets the other. I think that's what this politician was trying to get at but was disastrous in their execution. Christians know that the Spirit uses prayer to sanctify us. It's not just words in the abyss and it's not magical incantations either. It's conscious surrender and active communication with a living God. More importantly, it's obedience to our Lord.
Perhaps a stumbling block here is the concept of victory. You see, Christians could be seen as working backwards politically. When Christ died he said "it is finished." Our "actions" therefore are really offerings before the throne of a God who has already completed his work. In other words, we're not trying to achieve victory or a favorable outcome, rather we seek to do the will of our King. The victory was already secured. The goal was already achieved. Our evangelism is not the end-state. The resurrection was the end-state. Evangelism is our obedience. So this concept of prayer, of approaching God first, of surrender and religious worship, can be frustrating and contradictory to worldly thinking, especially to modern political action.