Laura McNamee, 27, was told by police that she had been threatened by loyalists.
Ms McNamee was identified on social media sites.
During Monday night's council meeting it was decided to restrict the flying of the Union flag from 365 days a year to 17. Unionists had wanted no change to the policy while nationalists had called for the complete removal of the flag.
A proposal for designated days was put forward by the non-sectarian Alliance Party and was backed by nationalists.
Ms McNamee accused the UUP and DUP of trying to browbeat Alliance by using scaremonger tactics.
"It has not worked," she told the council chamber.
"The use of the flag as a political football does nothing to support a shared future."