I'll agree that it's not about Christians' beliefs in particular, but about the norms of that time (although virtually all Europeans/Euro-Americans were of course 'good Christians', at least nominally). And those norms included regarding Native Americans as 'savages', and that was enough justification for just about any atrocity, including biological warfare. The Amherst letters make this point of view clear enough.
Regarding whether they acted upon this idea, your Straight Dope link is entirely inadequate. Even before receiving Amhersts' and Bouquet's instructions, those at Fort Pitt had already done it:
[...] Fort Pitt account books make it clear that the British military both sanctioned and paid for the deed. The records for June 1763 include this invoice submitted by Levy, Trent and Company:
To Sundries got to Replace in kind those which were taken from people in the Hospital to Convey the Smallpox to the Indians Viz
1 Silk Handkerchef
& 1 Iinnen do
See: Fenn, Elizabeth A. 2000. “Biological Warfare in Eighteenth-Century North America: Beyond Jeffery Amherst.” The Journal of American History 86 (4): 1552–1580.
When convenient, non-Indians could of course also be labeled as 'savages' so that otherwise not acceptable tactis could be used, such as against those savage Americans in the Revolutionary war:
"Dip arrows in matter of smallpox, and twang them at the American rebels, in order to inoculate them; This would sooner disband these stubborn, ignorant, enthusiastic savages, than any other compulsive measures. Such is their dread and fear of that disorderl'"
-- Donkin, 1777, Military Collections and Remarks (also see Fenn 2000).
Regarding lack of proof: it is not so surprising that not much evidence was produced to document such dishonorable acts when they did take place. Many or most smallpox epidemics were probably the result of accidents rather than intentional acts. But that is no excuse for the prevailing ethics of that time.