There are generally three community types: urban, suburban and rural. These words can be used as an adjective; and a noun to define the people living in that area. The OP wants a word for people that are not urban, that covers suburban and rural. There appears to be no common unambiguous word for this. There are many words for people living in the country (countryside) like rural, ruralist, rustic, rustical, countryman etc. (and many colloquial/derogatory words as well).
A rather neologistic approach would be using the words non-urban and non-urbanite (or without a hyphen) as a noun (as urban and urbanite are used as a noun also for a person who lives in a city or town) and it is possible to find usages online.
Throughout SEA, non-urbanites are increasingly relying on search to help them find the information they need, with two-thirds using search on their mobile phones. - thinkwithgoogle.com
Wiktionary has a definition for nonurbanite also:
One who is not an urbanite.
An unambiguous term (but not a single word) that can be considered is a non-city dweller which is used in formal contexts.
We examine the nature of government wage differentials for female workers separately for city dwellers and non-city dwellers.
Sharmila Choudhury (1994) Government wage differentials for women: do city dwellers earn more?, Applied Economics Letters, 1:3, 35-38, DOI: 10.1080/135048594358258