Final answer:
The practice of polygamy among Mormons in the late 1800s was considered an indication of their immorality, leading to significant societal tensions and the persecution of their founder.
Step-by-step explanation:
The aspect of Mormons that was considered to be an indication of their immorality in the late 1800s was the practice of polygamy. This practice, whereby a man could have multiple wives, was a significant deviation from mainstream Christian marital norms of the time and attracted considerable attention and outrage from other Americans. In addition to the unease prompted by their distinct theology and autonomous societal structure, polygamy was a lightning rod for criticism, fear, and the perception of moral corruption within the Mormon community. The controversy over Mormon polygamy contributed to significant tensions between Mormons and non-Mormons, leading to violence and ultimately to the arrest and death of Mormon founder Joseph Smith, Jr.