As governor of Kansas and a vocal opponent of marriage equality, Brownback revoked a previous governor's executive order that provided non-discrimination protections to LGBT state employees. He also signed legislation that would allow universities to discriminate against and exclude LGBT student groups.
LGBT Americans have a constitutional right to marriage equality, a fact reaffirmed by the United States Supreme Court several times. It's amazing how many Republicans are willing to look the other way when certain of their peers, including the President, are perfectly happy implying that LGBT Americans should be treated as second-class citizens and that their constitutional rights should be ignored.
I can't imagine they would be so cavalier if one of their members said interracial marriage was wrong or that the law should ban marriage between Christians and Jews. The Republican Party's selective hate is appalling.
At a minimum, Trump's nomination of Brownback once again proves the President lied. He is not pro-LGBT as he claimed during the campaign; he's clearly anti-LGBT, as his actions reveal.