The Washington Blade has a detailed story March 2 by Michael Lavers on LGBTQ immigration from Central America. The migrants flee drug-related violence and lawlessness, most of all probably from El Salvador.
The policies of Donald Trump certainly raise anxieties, but maybe not as much as people think – as there were so many deportations under Obama.
Central American culture is obviously very hostile to gender-related ambiguity, as the article notes.
Nevertheless, a local Arlington VA church, Mount Olivet, has in the past sent missionary groups to El Salvador.
Assistance for LGBT asylum seekers has tended to focus on sub-Saharan Africa (which is largely evangelical Christian rather than Muslim) and sometimes Russia, which passed its notorious law in 2013.