There are no ideas that are not commensense.
Ah. This is a case where you've re-defined a word to mean something that it doesn't normally mean, and forgot (and this is a generous interpretation) to tell us.
The statement is false. As the French say, "Les sense common n'est pas si common." You also have the absant-minded professor types who are VERY intelligent, but do things like walk onto busy streets because they were thinking about n-dimensional morphospace. There's also all the ideas in science which contradict common sense--for example, rocks are very, very weak over long periods of time, or the whole concept of singularity (meaning black holes, not computers and people).
But if science doesn't tell us 'which things we ought to explore' then how are we to choose among them?
Simple: we explore ALL OF THEM, in a systematic fashion.
I once found a rock in my dad's back yard. My family by and large said "Oh, look at the pretty rock!" I spent a few hours looking at the rock. Where they saw simply an innert lump of matter, I saw three different episodes of shattering and re-forming, over a few million years. I saw evidence of tonns of liquid-hot rock flowing through tonns of overburden. I saw water build up in the crystals and re-shape the chemistry. Where my family saw a pretty rock, I saw the story the rock had to tell. So yeah, we can wonder in greater detail.
the church was the backbone of science proper, and is still inseparable from it.
No. The church (and anyone who uses this term means Christianity) and science don't actually get along that well. And given the number of atheists in science, I think it's safe to say at minimum that the church and science are separate.