What does someone's opinion of gay sex have to do with their qualifications for Secretary of State?

Because the important thing isn't world peace, it's making gay/lesbo/trans the norm.

Not the opinion of the sex acts themselves, but the opinion of the PEOPLE who do such acts. That is important. Hard to be a decent (as in almost good) Sec of State and a totally judgemental prick. So, if you want the job, you might want to be a little more open to ideas that are different from your own, because you will be dealing with people every freaking day who disagree with your ideas and ideals. If all you will do is pass negative judgement, war will follow, and there is no need for that at all.

Does that answer your question or don't you actually want to know?

Because prejudice and bigotry should exclude anyone from holding this office, when persecution and murder of gays is happening in many parts of the world. Or is the claim that the Republican Party believes in "liberty and justice for all" is just a lie.

But then it should matter if the person appointed as Secretary of Education believes in the public education system. However in Trump World this is another thing which has no bearing on whether that person is suitable for the job.

As a conservative I would say because gay people are a part of the “State” he will be Secretary for.

The LGBT community are jailed or killed in some countries. One's view on if that is "moral" or not will influence how someone deals with these nations and whether or not they push those nations to reform or not. Not to mention that it also influences how we assist, or don't, other nations with HIV prevention and treatment.

What about his gay employees?

For that matter, is the best choice someone who is bigoted against a sizable amount of the population?

They want to know how the candidate will interact with gay world leaders.

Not a gosh darned thing.

Has to do with their ability to remain fair and unbiased.

Absolutely NOTHING.