Why put idols by the non-believers in a house built for worship of ONE-GOD?
I would not know. What you ask here is in essence deep fantasy. You would have to ask the author of that fantasy world, or perhaps its fans, knowing from the start that the answers would probably change from one perso to the next.
If you disagree, then it seems to me that it falls on you to give us some indication of how one could tell whether something is an "idol by non-believers" and, for that matter, also that there is a "one-God" and how he could be detected, as well as why people would be expected to agree on the existence of such a being.
But I very much doubt you can accomplish even one of those three goals. Or that anyone can. Because, after all, we are talking about a fantasy, not about the real world.
Now, indulging in that fantasy for a moment, let me try to answer anyway:
Is it fair on the part of non-believers?
There is no way to tell without the relevant information, which you did not provide. What would those idols be? Why exactly were houses of worship built in the first place? What social role or other significance would those houses have, and in which way, if any, are those idols detrimental to that role? Do they provide some sort of benefit, and if so how is it shared among the people exactly?