The show had just begun at the Alex Theatre in Glendale, Calif., when 600 people were rushed out.
The singer-songwriter has been a longtime supporter of the LGBT community.
The song from The Greatest Showman has become a hit at LGBT festivals for its message of empowerment in the face of hardship.
Watch the world premiere video of the chorus performing with singer-songwriter Maggie Szabo at L.A. Pride.
The founders of social justice-oriented Lighting in a Bottle emphasize inclusivity for all.
"May we end up in a world where everyone can live and love equally," Swift told her LGBT fans.