All political views are influenced by one’s religion or lack thereof. Politics is not a neutral arena. Both faith and unbelief are formative in one’s worldview. In the context of that worldview, one’s values emerge. And from those values one’s thoughts, words and deeds are born, which are inextricably tied to his or her political views. Therefore, unless freedom of religion is revoked, or people of faith are forbidden to serve in office, politics can never be devoid of religious influences.
But this is not necessarily a threat to religious freedom, nor does it necessarily violate the separation of church and state. Many of one’s political positions may be rooted in faith, yet at the same time intersect with the views of another, although arrived at by different means.
An example of this might be abortion. I arrive at my pro-life position largely in part to my faith. Yet there are atheists who support pro-life causes for entirely different reasons. When stating my political position on the issue, I am free to express that my position is faith-based, while the atheist is free to express his or her reason.
Expressing political positions does not require someone to surrender his or her reasoning behind those positions, even if it is explicitly rooted in religion. To insist upon this would, in fact, violate one’s religious freedom.