What portion of Northerners were against slavery for humanitarian reasons in 1860 America?

This is not an objective question, but I can tell you that the idealist abolitionists were mainly liberal elitists living in Boston and New York. The average farmer types in Ohio, Pennsylvania, New Jersey, etc, opposed slavery on grounds of principle, but also wanted to put a stop to the importation of Africans into the country and wanted them out of the country. They wanted both objectives accomplished. The sentiments can perhaps be summed up best by Abraham Lincoln:

...zeal for the spread of slavery, I can not but hate. I hate it because of the monstrous injustice of slavery itself.... it forces so many really good men among ourselves into an open war with the very fundamental principles of civil liberty.
....
If all earthly power were given me, I should not know what to do, as to the existing institution. My first impulse would be to free all the slaves, and send them to Liberia--to their own native land.... but its sudden execution is impossible. What then? Free them all, and keep them among us as underlings? ... What next? Free them, and make them politically and socially our equals? My own feelings will not admit of this; and if mine would, we well know that those of the great mass of white people will not.... We can not, then, make them equals. But it does seem to me that systems of gradual emancipation might be adopted; but for their tardiness in this, I will not undertake to judge our brethren of the South.

--- Abraham Lincoln, Peoria, October 16, 1854

If your question is how many in the North wanted to abolish slavery that would be very high. If your question was How many in the North wanted to go to war over slavery in 1860's; that would likely be much lower.

Given the facts that the North did not have slavery, and wasn't entertaining starting up slavery.. the number of folks in the north who opposed slavery and thought it was a brutal immoral practice were likely quite high.

I would argue that both the destruction of the whig party, and the creation of the new Republican party in 1854 were all about first the limitation of slavery(no new states should have slavery) and then the abolition nationally of slavery. The whig party went away because it proved ineffective in containing and ultimately banning slavery, and the Republican party was created as an abolitionist party to resolve this issue.

John C. Fremont, the first Republican to run for the Presidency in 1856 used the slogan "Free Soil, Free Men, and Fremont" crusading against slavery. So to your point, John C. Fremont, won 11 of the 16 Northern states on an abolitionist ticket. So closely were the Republican to the abolitionist movement the South threatened to secede if a Republican won the Presidency.. both of which happened in 1860.

So your question was: Approximately what portion of the population in the North in 1860 wanted to end slavery because it was a brutal practice that violated the human rights and dignity of slaves? I have no clue. But 70% of the northern states voted for the abolitionist candidate in 1856. And All 16 along with California and Oregon voted for Abraham Lincoln the abolitionist candidate in 1860.

So checking out the exact percentage by northern state which voted for Lincoln might give you a starting point.

looks like about 55-60% support in the north with Vermont coming in at 75.8%

I would further say that while most in the north were willing to let slavery die over a prolonged period by limiting their power in the congress and denying them new state members; after the supreme court decision of 1857, that started to change. The Dred Scott decision; radicalized the North as much as the reaction to the Kansas Nebraska act radicalized the mid west. The Dred Scott decision effectively legalized slavery in the north. Slave holders were free to bring their slaves to the north, and worse run rough shot over local laws in capturing "escaped slaves".. Or any free people of color they pleased. This was a pretty hard pill for the north to swallow and accounts for the rise in popularity of the Republican Party in the North leading up to the 1860 elections.

There were no public opinion polls, so obviously it is impossible to get an exact estimate. One good data source, then, is elections. The Liberty Party was supported by abolitionists with moral objections to slavery. (This is opposed to the Free Soil Party, which as OP has noted garnered support from those more concerned with white labor than black slaves.) So vote for the Liberty Party is a rough proxy of humanitarian abolitionist sentiment.

In the 1844 Election, Liberty candidate James G. Birney received 2.3% of the vote. Of course, he was not even on the ballot in most Southern states. In New Hampshire, Massachusetts, and Vermont, he received around 8% of the vote. In New York, Illinois, and Connecticut, he won only 3% of the vote.

Liberty Party vote may undercount abolitionist support, because the most radical abolitionists such as William Lloyd Garrison preferred to work outside of what they saw as a corrupt political system. So I'd estimate that in northern states in the 1840s, the percentage of humanitarian abolitionists ranged from 5-10%, and this number may have increased somewhat (though not dramatically) in the 1850s as sectionalism increased and attitudes toward slavery became more polarized.