> I take issue with the suggestion that an individual identifying with a major religion qualifies as adherence to its principles.
I agree that this an important distinction, but a person identifying with a major religion is a strong prima facie reason for thinking they're moral realists. Keep in mind that believing there are some moral facts is a much, much weaker position than believing all or even most moral claims of their religion are true.
> What's the case for moral realism that makes it so compelling?
My personal favorite are Moorean arguments of the form:
(1) Torturing people for fun is morally wrong.
(2) If there's at least one moral fact, then moral realism is true.
(3) Therefore, moral realism is true.
You can replace (1) with your favorite moral fact, such as
(1) The Nanjing massacre [1] was morally wrong.
(1) The torture and murder of Kelly Anne Bates [2] was morally wrong.
(1) The torture and murder of Unit 731 victims [3] was morally wrong.
and have the argument go through. The key point is that, as far as I know, there's no argument against moral realism whose premises are all more plausible than (1).
Another class of arguments are so-called partners in crime arguments [4][5][6], which link moral reasoning with prudential and epistemic reasoning.
[1] https://en.wikipedia.org/wiki/Nanjing_Massacre#Massacre
[2] https://en.wikipedia.org/wiki/Murder_of_Kelly_Anne_Bates#Mur...
[3] https://en.wikipedia.org/wiki/Unit_731#Activities
[4] https://www.tandfonline.com/doi/full/10.1080/000484008026364...
[5] https://www.tandfonline.com/doi/full/10.1080/00048402.2016.1...
[6] https://www.tandfonline.com/doi/full/10.1080/00048402.2017.1...