DDG says that a cleric must be of the same alignment as their deity (p 6):
WORSHIPPER'S ALIGN: This refers to the general alignment of those who worship, adore or propitiate the deity. This does not necessarily apply to the alignment of the deity's clerics, which must be identical with their patron's.
In the 1985 Dragon article that was mentioned upthread, Gygax says that
we are interested only in deities with followers dwelling on the Prime Material Plane of the campaign. These faithful give the various deities power. Of course, this idea is not new. It has been put forth often by others, whether seriously or as a device of literature. It serves as an excellent game device as well. (Dragon 97, p 8)
In an earlier issue (Dragon 92, December 1984, p 8), an article by Paul Vernon - "First, spread the faith: Clerics need to keep their mission in mind" - says that "The power of the gods is often proportional to the number of worshipers they enjoy". In the same issue (p 12), an article by Bruce Barber - "The more, the merrier: How clerics can 'find' new followers" - similarly says that
it seems reasonable to assume that the power of the gods, and perhaps their continued existence, stems from the number of worshipers that the deity can claim as his or her own. In a fantasy gaming milieu that utilizes many gods, this theory makes perfect sense.
I'm pretty sure these articles were the first time I encountered the idea, but as per Gygax's remark it seems likely to me that they're drawing on earlier works.