The believers say that God must take supreme importance in the world and in your life. God belief has content and implies content. It is not a bare belief.
Even when they support secularism, they teach that it is only acceptable in the sense that God gave the state a separate job to do from the Church. So even their secularism is religious, at least in intention.
They are saying, "We believers support the separation of Church and state on religious grounds. And because God asks for it. If our religion tells us different we will oppose this separation. We are open to being persuaded that our tolerance of separation is misguided or we have the wrong version. If God tells us to reduce or throw away the separation we will obey. We only accept because we think God wants us to. If we are wrong we will change our minds and act on that."
Their secularism only looks like secularism - it is not secularism at all.
Their secularism contradicts and therefore opposes authentic secularism.
It would confuse it.
Suppose God belief is important and good even if God does not exist It follows that belief must be still be protected, endorsed and maintained. How can secularists and atheists trust believers? They would clearly be too biased for politics or science.
Miracle claims are a crutch for such attitudes. A coincidence can make it look like a supernatural event happened. There are many cases in which such natural wonders were even more interesting than miracle stories. If we are committed to secularism, miracle claims and doctrines give us grounds for worry.