The Rev. tells TMZ Sports he's furious with the White House and press secretary Sarah Huckabee Sanders for saying Hill's tweets are a "fireable offense."

FYI, Hill strongly tweeted against Trump on Sept. 11 ... calling him a "white supremacist" and "the most ignorant, offensive president of my lifetime."

Sharpton says Hill has every right to express her political views without fear that the government will call for her job.

"Let's not forget, ESPN is regulated by the FCC. The FCC commissioners are appointed by the White House so it's a whole different level of intimidation on media outlets when you have the press secretary [calling for a reporter's job]."

Sharpton says he has a message for Hill -- "Stand strong. If they take you out, many of us in the civil rights community will stand up for you and take ESPN off our service."