In Octavia Butlers "Speech Sounds," how does the story’s central conflict and its resolution serve the story’s theme?

Well, there are a lot of themes in the story. Here are the ones that stand out to me:
1) The importance of language. In Rye’s world, most people can’t speak or read, and this inability to communicate verbally has turned people into animals. Rye and the bearded man are able to have a human connection because of their verbal abilities. It is the bearded man’s humanity that ultimately gets him killed, but Rye’s hope for the future is rekindled when she finds the children, both of whom can speak perfectly. The final words of the story, “It’s okay to talk to me,” reinforce how important words are in even the simplest acts of empathy and fellow feeling.
2) The hidden identity. Rye is an outsider, or “other,” in this society because she can think straight and talk. If this were known, she would be envied and probably a target for violence, so she is very careful to keep her abilities secret. What binds her to the bearded man is that they share the same secret (relative un-impairment); when she finds the children, her decision to raise them is based in part on recognizing that their ability to speak needs to be protected or shielded from others. In this sense, the final words of the story suggest that she is creating a safe space for them, and that in her small way, she is trying to bring civilization back.
3) Trust. An essential component of Rye’s world is mistrust—no one is to be trusted. This is in part because most people have lost the use of language, so, beyond crude gestures, it is impossible to know what someone’s intentions might be. Part of what makes the bearded man different is his ability to listen to Rye’s needs: he asks her which way to go in the car, and, more importantly, does what she says. The best example of his understanding her needs is when he produces a box of condoms: Rye is so surprised and delighted that he has understood her, she actually giggles.
In each case, the conflict (Rye vs society) serves to highlight what is lost when people lose language. In a similar vein, the resolution (Rye’s finding the children who can speak) suggests that language is the essential component for rebuilding human relationships and, presumably, civilization.