Please message me with additional resources to add, if you know of LGBT friendly organizations.
National Coalition of Antiviolence Programs has a list of partner organizations that are LGBTQ friendly, many of whom offer resource for sexual assault survivors.
RAINN runs a national hotline (1.800.656.4673; online hotline). Please note: RAINN works with many partner organizations and survivors have reported experiencing transphobia from some of these. If you are trans* please check out the resources below, which have been reported to be trans* friendly.
Bay Area Women Against Rape (Oakland)
Community United Against Violence (San Francisco, LGBTQ specific)
Peace Over Violence (Los Angeles area)
Center on Halsted (Chicago, specifically for LGBTQ folks)
Rape Victim Advocates (Chicago)
Kansas City Anti-Violence Project (serving western Missouri, Kansas, Nebraska, and Iowa, specifically LGBTQ)
Network/La Red (Boston, LGBTQ specific)
Sexual Assault Support Services (Eugene-Springfield)
The Northwest Network (Seattle, LGBTQ specific)
2110 centre for gender advocacy in (Montreal, Quebec)
519 Church Street Community Center (Toronto, Ontario, LGBTQ specific)
Klinic Community Heath Center (Winnipeg, Manitoba)
Sandi Merriman House (Victoria, British Columbia, emergency shelter for women, trans* friendly)
UK (with the exception of the Edinburgh centre, I don’t know how LGBTQ friendly these places are):
Edinburgh Women’s Rape and Sexual Abuse Centre (Edinburgh)
Rape Crisis (England and Wales)(seems oriented toward women and girls specifically)
Survivors UK (London, male survivors specific)
This list was compiled using the list at Questioning Transphobia, as well as my personal research, and input from followers of the blog.