Why do you think the Republican Party gave up on supporting civil rights for African Americans in this era?

The correct answer to this open question is the following.

Unfortunately, you did not mention the "era."  It could be many eras or times in history.

However, trying to help you, we are going to assume that you are referring to the American Civil War era, from 1844 to 1877. During this time, African Americans were accepted to join the Union Army. Republicans in Congress supported African Americans in that they agree on the abolition of slavery in the Southern states and grant them civil rights.

After the war and during the Reconstruction time in the South there was a group in Congress known as teh Radical Republicans that did not agree with the Reconstruction Plan issued by President Lincoln because they considered it was so simple. These Radical Republicans in Congress thought that the South deserved a harsh punishment for the pain and destruction created during the Civil War.

During this time, Republicans supported the decision to send the Army to the south to protect African Americans and their civil rights, although this situation changed with the Compromise of 1877 when Republicans accepted to remove the troops from the South.