It is doubtful, in the extreme, that if Abraham Lincoln was alive today that he would be accepted, or would want to be a Republican. He certainly could not be their candidate.
"Labor is prior to, and independent of, capital. Capital is only the fruit of labor, and could never have existed if labor had not first existed. Labor is the superior of capital, and deserves much the higher consideration." -- Lincoln's First Annual Message to Congress, December 3, 1861.
"We may congratulate ourselves that this cruel war is nearing its end.
It has cost a vast amount of treasure and blood. . . .
It has indeed been a trying hour for the Republic; but
I see in the near future a crisis approaching that unnerves me and causes
me to tremble for the safety of my country. As a result of the war,
corporations have been enthroned and an era of corruption in high places
will follow, and the money power of the country will endeavor to prolong
its reign by working upon the prejudices of the people until all wealth
is aggregated in a few hands and the Republic is destroyed.
I feel at this moment more anxiety for the safety
of my country than ever before, even in the midst of war.
God grant that my suspicions may prove groundless."
-- letter from Lincoln to (Col.) William F. Elkins, Nov. 21, 1864.
Lincoln saw the danger of the moneyed interests controlling government. The contractors for the war became rich and so began the era of robber barons that lasted to the twentieth century. To secure (steal) a presidential victory in 1876, the Republicans ended Reconstruction in exchange for Florida's electoral votes and turned their backs on the negro. At the turn of the century the McKinley - Theodore Roosevelt government made the country an internationalist and imperialistic empire through wars with Spain and the Philippines. The bearer of the Democracy*, William Jennings Bryan, lost three presidential elections, the first probably stolen. The progressive era lasted for only a few years before the Great War†. The 1920s were a return to robber republican hegemony. Calvin "Silent Cal" Coolidge uttered the essential fascistic statement, "The business of government is business.". The Republican party has shown a remarkable consistency since the death of Lincoln. Not a new thought in a century.
*at the time, many Democrats called the party -- the Democracy
†World War I