I ran out of steam after the 10th random homeless shelter that I couldn't find an answer about them accepting queer families or trans people.
A few orgs that are pro-lgbt (I encountered the acronym "LGBTQ2S+" for the first time, I have learned that "2S"/"two-spirited" is a gender identity in some indigenous-American cultures).
A few faith-supported orgs, which isn't a problem in itself, but I'm suspicions. Only clear negative signal I was an org that was "Compliant with Executive Order 14168"