The group said it made the video private out of concern for its members' safety.
In it, the chorus seemed to blame conservative media for the backlash.
"The far-right conservative media found our ‘Message…’ video and have taken it as their cause … They have taken the lyrics out of context to support a narrative that suits their intolerant and hateful needs," the message read.
Republican Ohio state legislator Christina Hagan said:
"They are pompously singing about undermining traditional values of families."
The group defended itself, calling the video 'tongue-in-cheek humor'.
PODCAST EXTRA: Listen to this gay conservative PUSH BACK against 'coming for your kids' narrative live on the 'Kelly Golden Show' on 94.3 WSC ...