I'm not sure what you may mean by "the usual rules".
The word
communities is a perfectly good word, so I don't see how it would be restricted to the singular.
In the singular, however, the only choices for an article are
a or
the. Not having any article is not an option.
an alternative to a non-believing military community
means that the author doesn't know which community or doesn't want to
tell us which one or doesn't think it's important to tell us. The
reader is reasonably expected to ask "Which non-believing miliary
community? (of several)".
an alternative to the non-believing miliary community
means that the author expects the reader to know exactly which
community he is referring to. In all probability he wants us to
think the community consists of
all military people who are not believers.
supported by a local community means
supported by one of the communities in the vicinity
(of the event), and the author does not think it is important to tell
us exactly which one. The reader could reasonably be expected to
wonder which local community the author was referring to.
supported by the local community means
supported by that community in the vicinity (of the event) which everybody knows about or can easily deduce. The reader is not expected to ask
which community
if this wording is used. The reader is expected to figure it out
on his own. Almost certainly, the author means the very community
in which the event took place.
CJ
P.S. Very briefly, the presence of "the" tells the reader (or
listener): Figure it out for yourself! Something you know
about this situation or other situations you've experienced in life or
something I've written (or said) previously about it is enough so that
you can figure out for yourself exactly what I'm referring
to.