No, the Republican Party rose out of the dissolution of the Whigs, who then joined together with the Know Nothings. There were abolitionists in the party, no doubt, but it was the party that took over from the Whigs and adopted Henry Clay's corporate welfare philosophy, called the American System by Clay as a PR strategy, adopting it more broadly than ever before.

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Lincoln was their first candidate.

No, Lincoln was not their first candidate. The first Republican presidential candidate was John Fremont in 1856. Fremont was, among other things, a strong abolitionist but was very unpopular with the Whig Party stalwarts that came to the Repubicans. Lincoln had little use for Fremont as well, and when Fremont, commissioned a General in the Union Army, freed slaves in an area he was given command to administer, Lincoln fired him and ordered the slaves returned to their owners.

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A large majority of the Christian folk who fought and died in the Civil War thought, rightly or wrongly, that they were freeing the slaves--the Abolition Party.

Not only were abolitionists a minority in the northern states, estimated at no more than 5% of the voting citizenry, they were even less represented in the Union Army. After the Emancipation Proclamation was issued, there were mass dissertions in some regiments in the Union Army from the resentment caused by it.

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The 'Emancipation Proclamation' and the fact that the single greatest product of the Civil War was an end to slavery only bolsters that conclusion...

Slavery was ended by the passage of the Thirteenth Amendment, and nother else.

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Surely there were other motivations but they were not the motivations that encouraged the common folk to fight and die...If it wasn't about slavery, why didn't the Republicans call themselves something besides the 'Abolition Party'?

That would be because the Republicans never called themselves the Abolition Party to any extent. Possibly John Fremonts weak faction used that term, but it's so rare as to be virtually unknown by others.