Samar Habib has a rather alarming story in the Washington Post Monday, Nov. 28, “The Trump/Pence Administration will likely switch sides on global LGBT rights”, link here.
Pence, who has attracted attention for talking about conversion therapy in 2000, is now quoted as saying that gays (LGTBQ) should be left alone as individuals but not singled out as a class for protection. Under Obama, the US has been able to promote the class idea in some marginal countries.
Nevertheless, Russia, for example, has become much more anti-gay under Putin, passing an anti-gay propaganda law in 2013 that seems motived not just by equating homosexuality to interest in minors, but specifically to fears about low birth rates.
Trump says that gay marriage is settled law and does not bother him, but that gays and lesbians, like anyone else, need security at home from militant violence from foreign sources, mostly tied to radical Islam.
Trump and Pence seem to suggest that involvement in anti-gay policies of some countries (like in Africa) could complicate other relations with those countries, but anti-gay policies overseas can seriously hamper business and charitable work now. It could lead to more asylum claims at home.