Question

I don’t understand why the assumption that the world is ideal is relevant.

The assumption that the world is ideal is relevant because today it is impossible to grant a religious court the authority to beat you at its own discretion, and religious courts also do not intervene in the areas of Orach Chayim and Yoreh De’ah.

I also don’t understand the distinction between the grounds, nor why it is relevant to the question.
One could argue that only with regard to a universal right (returning stolen property) would the religious court hear the claim even if the plaintiff does not observe Jewish law, because it was not Jewish law that granted him that right; rather, he would be entitled to it even if there were no Jewish law.
By contrast, with regard to a right created by the Torah (support payments), the religious court would not hear the claim if the plaintiff does not observe Jewish law, because it is specifically Jewish law that granted him that right, and he would not be entitled to it if there were no Jewish law.

In principle, a religious court is supposed to hear every claim regardless of the character of the plaintiff.
That is, is the religious court forbidden to use refusal to hear a claim as a sanction to compel observance of the commandments?