Soul music started as a secularized form of gospel music, and tended to retain from its roots a certain spiritual quality and concern with moral uplift, although it also added a physical sensuality, and often dealt with themes of romance, lust, and occasionally vice. Although the genre began in the 1950's, with artists like Ray Charles and Sam Cooke, it really came of age in the late 60's and early 70s. This was a time of great political upheaval and rapid social changes in America, particularly centered in the black community around the fight for civil rights. The political victories in the late 60s paved the way for a new sense of black pride and unity as the 70s matured. All of this inevitably made its way into the lyrics. Everyone from Isaac Hayes, Curtis Mayfield and Sam Cooke to Stevie Wonder, Aretha Franklin and the Temptations began to put veiled or explicit expressions of black pride, political activism and general uplift into their lyrics. This paralleled a similar trend in mainstream American pop music, with artists like Bob Dylan, the Beatles and CSNY all putting out politicized anthems.
The musical echo you hear in Sesame Street is a reflection of its contemporaneous beginnings (1969) --Sesame Street often sounds like the 1970s. Similarly, the bold African-American hairstyles and fashions of the 70s were enormously influential, and were often adapted by later artists such as Snoop Dogg, even when the music was quite different. Poets like Scott-Heron were also a major influence on the development of rapping, which is essentially long-form narrative poetry over a beat. Nor did the political activism entirely die out --there's a long and continuing tradition of politically conscious hip-hop, although typically with a more militant edge, and a less hopeful and positive outlook.
It's worth noting that the now pervasive narrative of black family dysfunction is NOT native to the black community. It was imposed externally by the mainstream media, and hadn't yet been internalized in the 70s the way it was for the generation that matured in the 80s and 90s. (This was also before the crack epidemic, and relatively early in the hypocritical and racist "War on Drugs," which combined to cripple the previously stronger black family unit.) In the 70s the black community was vocal about external oppression, but largely feeling very positive about itself and its chances of advancing and succeeding --a feeling perhaps best encapsulated by the iconic anthem "Ooh, Child". In truth, there was a lot to feel good about in the 70s. Over a decade of difficult, dangerous and often deadly struggle had finally brought about an end to legalized segregation and discrimination. The slogan "Black is Beautiful" had begun to gain traction, even among white tastemakers, and black artists were beginning to be able to achieve crossover success without the heavy concessions or outright whitewashing of previous generations. The 70s rhetoric was a direct response to centuries of disempowering messages aimed at the black community in the slavery and post-slavery eras: Black is weak, ugly, inferior, powerless, divided, despised, servile, obedient and doomed. Therefore the messages you hear in this music are aimed directly at countering these. These songs are saying that black is strong, beautiful, superior, powerful, worthy of respect, resistant, rebellious, and aimed at a brighter future.