The first task is to define or at least comment on "language community." Various approaches and various individuals in linguistics define language community, more recently identified as "speech community," in various ways, many of which seem contradictory. For example, Labov identified Philadelphia as a language/speech community in 1989 while London was not given this statues by Wardhaugh in 1998.
That said, for a language community to be impacted by both accent and dialect, it will be a diverse one, perhaps a large one (though not necessarily). Two dominant points of significance particularly related to accent are prestige and negative prestige. Another such point but particularly related to dialect is inclusiveness versus exclusiveness.
Accents (as well as dialects) bestow prestige or negative prestige. Labov demonstrated that women tend to opt for the accent above their own socioeconomic status in order to attain increased prestige. Conversely, men, perhaps from a greater competition related fearfulness, often opt for an accent lower than their own, thus embracing negative prestige, or a loss of prestige (these phenomena are still being investigated). This example illustrates that accent within a language community may be chosen and may be the instrument of rising or descending in social status within a community. This has vast significance for economic and educational opportunities as well as stereotypes and psychological well being.
Dialects (as well as accents) trigger inclusion into groups and exclusion from groups. While accents may have the same effect in a language community, dialects have the potential for far greater effect. Some dialects are so exclusionary that non-speakers cannot communicate with, or have trouble communicating with, dialect speakers. While dialects of any level of divergence from the Standard language may induce inclusion/exclusion, some result in dramatic exclusion thus exacerbating the significance dialects can have on the dialect speaker's educational, economic, social and psychological opportunities in a language community.
Of course, the reverse can occur if a Standard language speaker enters a language community where the dialect or accent is the prestigious norm. In this situation, the Standard speaker can lose felt (as opposed to linguistic) prestige and be excluded from opportunity and socialization. Such exclusion has a similarly significant effect upon economic, social, and psychological opportunities and well being.
One community in which accent is extremely important is that of English universities and professional cohorts. Professor Higgins in George Bernard Shaw's Pygmalion famously said:
"The moment an Englishman opens his mouth, another Englishman despises him."
English systems of social stratification over the past two centuries have had clear accent indicators, with the "received pronunciation" (RP or BBC English) indication the upper and upper middle classes and various regional accents signaling lower middle or lower classes. Many of the more lucrative professions, clubs, elite universities, and other areas where prestige affects entrance or promotion standards, those who speak using the RP have a significant advantage. Similarly, use of "posh" pronunciation would be unacceptable in working class social settings, especially in the north and midlands.