Taking a case is different from outright barring state authorities from accessing evidence.
See the Luigi Mangione case for an example of state having free access to evidence even in a federal case... Feds don't seem to have any trouble with sharing evidence there.
I'm torn on this - Christianity (particularly evangelical christianity) has had an extremely negative effect on democracy in our country and has caused physical harm to others.
However, I think most people with a conscience subscribe to some form of philosophy or religion (even if atheists aren't "loyal" to any particular perspective and may not even use titles/categories to describe their value system) and I think it's fine for your morals/conscience to influence decision making. Even a purely scientific decision making process could be considered a form of philosophy.
That being said, most organized religion is about obedience to the tenets of said religion, not a method of asking questions about the world to try to find the most just way to proceed.