Final answer:
The 10-letter word for the Rastafarian hairstyle that became fashionable in the 1960s is 'dreadlocks.'
Step-by-step explanation:
The 10-letter word for a Rastafarian hairstyle that came into fashion around 1960 is dreadlocks. This unique hairstyle has played a significant role in Rastafarian culture, symbolizing spirituality and a rejection of conventional beauty standards and societal norms. The hairstyle has been embraced by various subcultures and movements over the years, often associated with a non-conformist lifestyle. In contrast, hairstyles such as muttonchops, beehives, and crewcuts represent different cultural and historical contexts and are not directly associated with Rastafarian culture.