Trump appears to be of the strain of conservative thought that believes that gender equality has already been achieved, or even that the balance has tipped too far in the favour of women. Given this and his persistent annoyance at having his extremely misogynistic remarks referenced during the campaign it seems likely that he will seek to rollback any gender equality initiatives at State Department level.
Trump will not fire the workers of gender equality workers. To fire such workers, he would need strong reason to do so.Even if he did, there would be a huge backlash.It is clear by Trump's actions that what he said in the campaign is not always to be taken seriously.
The president elect Donald Trump is not that insane as people have been made to believe. I don't think just because he asked for the names of the gender equality workers he is going to fire them. Maybe he has his own reason but not firing them, remember America is a country governed by Rule of Law.
Trump became the President to work on economic issues. He wanted to make it clear that he would work on reducing barriers to work. He decided not to deal with social issues. Trump is going to look to the public pulse and let the people dictate what standards society will have. This means gender equity will prevail in Trump's administration.