Publishing in 1829, the evils of slavery were publicly condemned by George Moses Horton, who was the first black poet to do so.
Seems to be a case of modifier errors at the beginning - let's check the choices.
A) Publishing in 1829, the evils of slavery were publicly condemned by George Moses Horton, who was the first black poet to do so.
Opening modifier error, Who or what is 'publishing'? Can't be evils of slavery - reject
B) George Moses Horton, whose work was published in 1829, was the first black poet to condemn publicly the evils of slavery.
Seems good - but lets quickly check the other choices
C) George Moses Horton, publishing in 1829, condemned the evils of slavery publicly and was the first black poet to do that.
Meaning error, usage of 'publishing' is wrong
D) Publicly condemning the evils of slavery, George Moses Horton was the first black poet to do so
and he was published in 1829.
Run-on error
E) George Moses Horton, who was published in 1829, was the first black poet who publicly has condemned the evils of slavery.
Meaning error, usage of 'who was published' is wrong
B is our winner!