Would it be still appropriate, today, to call the the Republican Party the party of Lincoln, considering Lincoln's viewpoint on slavery and civil rights?

In my view, this question is less of a historical question and more of a political statement. When people ask if the GOP today is still the “party of Lincoln,” what they are really trying to do is to argue modern-day Republicans are anti-black, while Lincoln was pro-black. This is, in my view, unhistorical. 
The reason for this is that the issues facing Lincoln are nothing like the issues surrounding race today. In Lincoln’s day, the main racial issue was slavery, not civil rights. Of course, Lincoln was strongly opposed to slavery. He was not a fan of what we would call civil rights today. He did not believe blacks and whites were equal, and he did not believe that they could live together as equals. As he said in one of his famous debates with Stephen Douglas,

I am not, nor ever have been, in favor of bringing about in any way the social and political equality of the white and black races.

Because Lincoln believed these things, it is really not historically correct to say Lincoln would have held the same beliefs on civil rights that Democrats do today. Lincoln’s own beliefs would be completely anathema to both Republicans and the Democrats today. Of course, if Lincoln were alive today, he might have different views, but we can only speculate on what those views would be.
The Republican Party today does not hold all the stances Abraham Lincoln did, just as the Democratic Party does not believe, for example, in everything Woodrow Wilson believed in. As issues change, parties change. That is natural. We cannot logically argue the Republican Party has abandoned Lincoln’s ideas on race because Lincoln did not have to have opinions on issues like affirmative action, welfare, or Black Lives Matter, topics at the heart of conversations about race today.
https://www.history.com/news/5-things-you-may-not-know-about-lincoln-slavery-and-emancipation