Answer:
The two reasons that Know-Nothings believed being Catholic was incompatible with being a United States citizen are that Catholics weren't compatible with Protestants neither did they want to be ruled by Americans.
Step-by-step explanation:
The Know-Nothing was a political party in America prevalent during the late 1840s and early 1850s. This party was also known as American Party.
The American Party was in staunch opposition to the immigrants and Catholics. The two reasons that the Know-Nothings considered Catholic being incompatible with being United States citizen was because Catholics were not in agreement with Protestants, they despised Protestants. Other reason is that Catholics didn't want to be ruled by Americans.
This is why Know-Nothings believed Catholics as incompatible with being United States citizen.