You are exactly right. The industrialists (broadly speaking) didn’t really give two hoots about slavery. What the northern industrialists wanted were protective tariffs, so that European goods would cost a lot more, forcing colonists to buy goods made in American factories through simple economics. But the southern plantation owners opposed tariffs, because tariffs enacted on goods coming into America from Europe meant that European nations would counter with tariffs on goods going in the opposite direction. This made American cotton and tobacco, produced in the South, more expensive and made it more difficult for the southern plantations to compete with tobacco and cotton produced elsewhere.
The industrialists didn’t have the votes to get their protective tariffs. They had been members of the Whig party, which favored economic protectionism and modernization. But the Whig party started to collapse in the late 1840s and early 1850s, largely over the issue of slavery.
At the same time, you had the abolitionists, who opposed slavery, but also did not have enough votes on their own to push their agenda forward.
So the two groups joined forces against the southern plantation owners. The northern Whigs and the abolitionists got together and formed the Republican Party. While the industrialists didn’t really care too much about slavery (though to be fair, some did, just because they were also abolitionists), and the abolitionists really didn’t care too much about industry, by joining together, they could get enough votes that they could both get what they wanted.
You can see the split in party politics if you read Lincoln’s speeches. When he addressed primarily industrialist groups, he pushed the tariff issues and downplayed the party’s anti-slavery platform. When he addressed abolitionists, he did the opposite, downplaying tariffs and emphasizing anti-slavery rhetoric.
The Republican platform in 1860 ended up therefore being the opposition of slavery, protective tariffs for industry, a homestead act so that the new western territories which were becoming states could be settled, and the construction of a railroad to the Pacific.
Lincoln did promise that the South could keep its slaves. But he refused to back down on his promise that all of the new territories would become free states.
In any event, by ganging up, the former Whigs and the abolitionists together managed to get enough votes to win the 1860 election.