Safe Responsible Ethical Scientific Endeavors Assuring Research for Compassionate Healthcare Act or the Safe RESEARCH Act This bill amends the Public Health Service Act to prohibit the use of tissue from an induced abortion in research conducted or supported by the National Institutes of Health (NIH). Research with human fetal tissue or alternatives to human fetal tissue (e.g., stem cells) conducted or supported by the NIH must meet requirements currently applied only to research on the transplantation of human fetal tissue for therapeutic purposes, including requirements for the informed consent of the donor and researcher. Research conducted or supported by the NIH may use human fetal tissue only if the tissue was obtained in accordance with state law regulating anatomical gifts. Currently, executive branch officials may not prohibit the NIH from conducting or supporting research on the transplantation of human fetal tissue for therapeutic purposes. The bill repeals that limitation on executive branch officials. The bill repeals a requirement that the NIH fund certain proposals for research on the transplantation of human fetal tissue for therapeutic purposes.