Did the union soldiers fight against slavery?

Answer 1

The first answerer said, "No."
The common consensus would be that it was indeed fought over slavery, but of course the South was FOR slavery, and the North was AGAINST slavery.

There were other underlying tensions, particularly about State vs. Federal rights.
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Answer 2

Most of them did not enlist in order to fight slavery. They were fighting for the integrity of the Union, partly because they held it sacred, and partly because they wanted the vast cotton revenues back.

When the Confederates looked as though they were winning, the British showed an interest in granting recognition and sending military aid.

This was Lincoln's biggest worry, and the only way to deter them was to turn the war into an official crusade against slavery, so that free nations abroad could not aid the South without looking pro-slavery themselves.

So he issued the Emancipation Proclamation as an urgent tactical war-measure, but also hoping that the Northern public would feel inspired by it. The mid-term elections showed that they did not.

Meanwhile the Union troops were now licensed to free any slaves they came across, and it is reasonable to claim that a good many of them began to see that slavery was yesterday's system. General Sherman, not exactly famous as a human rights activist, declared that the planters could no more get their slaves back than revive their dead grandfathers.