Here is another responsum, by R. Israel David Harfenes, Nishmat Shabbat, vol. 5 no. 500:4.
The author is asked if you can violate Shabbat to save the lives of irreligious Jews who came from the former Communist countries, that is, Jews who never had the benefit of a Jewish education. His answer is absolutely not, and he questions whether it is even permitted to save their lives during the week!
…Harfenes also throws in that one who doesn’t believe in the Rambam’s Thirteen Principles is among those who should be killed. Taking a line from the Inquisition, he adds that killing these people is actually good for their souls, not to mention a benefit to the community at large.
…In a previous responsum, 400:1, he discusses the same question with regard to the typical secular Jew and concludes likewise that one cannot save them on Shabbat. The only heter he can find is that if the haredi doctors don’t save them, then the secular doctors will refuse to save haredi patients. But unbelievably, rather than seeing this as a natural reaction of the secular Jews upon learning how people like Harfenes don’t value their lives, and are even are prepared to let them die, Harfenes sees this as an example of anti-Orthodox hatred!