Did people truly believe black people were descended from Cain? How widespread was this thought?

Proportions are hard to estimate. There wasn't a lot of position polling going on in the the 19th century. But we can tell from some writings that it was widespread and popular. Two groups in particular seemed to push the point, the Southern Baptists and the Mormons.

The Baptists of course didn't have a tradition of centralized leadership so it's hard to say how deep the belief went in individual congregations. But books like Josiah Priest's Slavery as it Relates to the Negro or African Race from 1843 were popular best sellers. And the break in 1845 between the Northern and Southern Baptist branches was largely over race, including the doctrine of the descent from Cain. In 1995 the Southern Baptist Convention formally apologized for its history of racism including the idea of a black descent from Cain.

The LDS racial tradition (which I am more familiar with) followed or paralleled the Southern Baptist tradition. Their scriptures, particularly, the Book of Abraham states that the wife of Ham (traditionally the biblical ancestor of the African peoples) was a descendant of Cain. God supposedly specifically preserved Ham along with the rest of the family of Noah so that the curse of Cain would not disappear. This 1881 quote from, then leader of the church, John Taylor sums it up:

And after the flood we are told that the curse that had been pronounced upon Cain was continued through Ham's wife, as he had married a wife of that seed. And why did it pass through the flood? Because it was necessary that the devil should have a representation upon the earth as well as God.

For anyone who is interested in Mormon racial history I'd highly recommend Armand Mauss' excellent All Abraham's Children: Changing Mormon Conceptions of Race and Lineage.

I'm not sure that rises to a burden of proof that a majority ever believed that blacks descended from Cain. Northern pastors wrote counters to Josiah Priest, and of course the Mormons were a small minority religion off in their own corner of the country. The idea certainly had support even in the North. But I suspect that the belief never rose to the level of a majority belief for the country as a whole.