The sentence states that an amendment was adopted to achieve a specific purpose, essentially.
The Equal Protection Clause of the Fourteenth Amendment (1868)
had been originally adopted in order that blacks in the post-Civil War South be given the full benefit of citizenship, but over the past century and a half they are expanding it to include all categories of civil rights.
A is incorrect because the first clause doesn't convey the full intention of the adoption in a grammatically correct manner. X was adopted TO achieve Y
In addition, "they" has no clear referent.
B) was originally adopted
to give blacks in the post-Civil War South the full benefit of citizenship
, but over the past century and a half
it has been expanded to include
B is correct because it clearly and grammatically states the intention of the adoption, then a second independent clause is correctly connected via "[,]+ [FANBOYS]" structure
C) had been originally adopted to give blacks in the post-Civil War South the full benefit of citizenship, while over the past century and a half was expanding it to include
C confuses the tenses, incorrectly, by stating that the adoption occurred while the expansion was occuring.
"was expanding" has no clear reference either. Who was expanding?
D) had been originally adopted to give blacks in the post-Civil War South the full benefit of citizenship, and over the past century and a half has expanded to include
D incorrectly joins the dependent clause with a comma. There is no need for this.
Plus we should prefer the independent clause in B to D
E) had been originally adopted by giving blacks in the post-Civil War South the full benefit of citizenship, and over the past century and a half they have been expanding it to include
the first clause in E communicates that the amendment was adopted by DOING X (giving blacks in the post civil war south,...), which is obviously miscommunicating the logical meaning.
Again, "they" is incorrect