The 31-year-old seemed to be responding to a recent comment made by her former bandmate Josh, where he called homosexuality "a perversion."
While she didn't name Farro directly, she did suggest that his views were responsible for his departure from the group in 2010.
"There's a reason there are only 3 people left in Paramore. Surprise, haters, it ain't cause of me," she wrote. "Paramore do not condone religiously/politically dogmatic beliefs which leave our LGBTQ+ friends, fans, & family feeling abandoned and hopeless."
"If that doesn't jive with you, well, feel free to go to where all past members of Paramore have gone which is literally anywhere else but Paramore."
While Zac Farro left Paramore with brother Josh back in 2010, Zac later rejoined the group, with the current line-up consisting of him, Williams and Taylor York.
Hayley concluded her posts by sending a message directly to Brian J. O'Connor - the creative director of her Good Dye Young hair dye company - writing, "To Paramore's LGBTQ+ family, you are full of love and you are loved."
Back in 2011, Hayley admitted her breakup with Josh was partly to blame for causing tension within the band. They split during the "Riot!" cycle. "It was really hard, because we were all friends, and then going through a breakup and going through any kind of tension as a band," she said back then.