Having been a Hatzolah member who was Mechalel Shabbos for goyim because of Aiva I think maybe I have a little to contribute to that conversation. Again...we are mechalel SHABBOS, YOM KIPPUR etc for goyim because of Aiva...we can surely stop your minyan for it. You are absolutely clueless!
I will hopefully have video evidence sometime next week.
According to the strict letter of Halacha saving a non-Jews life on Shabbos by doing a Melacha (forbidden acts) is not permitted; To quote the Kitzur Shulchan Aruch 92:1 "Shabbos is pushed aside for Sakonas Nefoshos (life & death situations).. therefore it is a Mitzvah to desecrate Shaboss for a Kosher person (even if he sometimes does sins) who is in mortal danger" (See also the uncensored Shulchan Aruch Yore Dei'ah 158:1).
One of the answers above misrepresented R. M. Feinstein's words by saying "To quote R' Moshe Feinsten, "A refusal to treat a non-Jew on the Sabbath would be totally unacceptable...", the impression is that is is Halachikly unacceptable when in reality he's saying that it is socially unacceptable. In the Teshuvah itself RMF says to try to avoid the situation and he's only talking about a doctor who by law has the obligation to heal the sick or otherwise face repercussions. In the end he concludes with the words "one can rule that it (inaction by a doctor) is like a Sakanah (danger) and therefore one may permit it".
For a short synopsis of some of the sources mentioned in the aforementioned answer, see Shearim Metzuyanim Bahalacha 92:1, 1) He brings an argument between the Pri Megadim who says we do not desecrate Shabbos for one who doesn't keep Shabbos Litai'ovon (for convenience reasons) and the Maharam Shik who is not sure about it. 2) He quotes the Pri Megadim who says that we do not desecrate Shabbos for a non-Jew and for one who doesn't keep Shabbos Lihach'is ('to anger G-d'). 3) He quotes the Chassam Sofer who says it is probably Halachakly permissible nowadays to ride in a wagon driven by a non-Jew to heal a non-Jew since inaction will cause the non-Jews to hate us for it and it may lead to danger for Jews. 4) He quotes the Divrei Chaim who says that a doctor is only allowed to desecrate Shabbos by doing actions prohibited by the sages but not by doing actions forbidden by Torah law. 5) He quotes the Yad Sholom who says that if by government law the doctor must desecrate Shabbos even by doing actions forbidden by Torah law, it may be permitted.