It sounds as if you want to make abortion strictly a personal choice, which is what it is now: abundantly available. What’s wrong with suggesting the Jewish position for all of society? It is certainly more moral, more thoughtful, than what we have now. What a Jew would be saying is not, “You must do it my way OR ELSE,” but rather, “Here is what I strongly recommend; this is what I consider moral, and I am choosing a candidate who reflects that morality, because abortion is a decision which involves more than just the mother, or even the couple; it impacts society to have a casual attitude toward life and death. As Jews, we believe that society (not just Jews) should have higher standards of life and death than what is currently operative in this country.”
There are many legislative proposals & private policies out there that cannot accommodate all religious beliefs. A decision reflecting a unity of purpose must be made. So, for example, a hospital may allow a variety of medical responses about certain eventualities, in concert with what the patient/family desires, but it will stop short of what the hospital considers unethical even if the family were to choose such an option, and consider such an option their “private morality.”
There are too many behaviors and decisions in society which are not mere private matters. And the laws we currently have reflect certain ultimate standards of behavior, even though they don’t cover, of course, all behavior. There is a point in society at which we can, and should, say No. And there are not a dozen different “no’s” we can have, depending on one’s religion. Choices have to be legislated which will have a degree of uniformity for all religions.