On Tuesday night, the group of 115 people had tried to take refuge in a single house, but was eventually taken to the church by police minibus.
Anna Lo of the Alliance Party said the families were "very frightened".
Ms Lo said attacks on Romanian homes - which included bricks being thrown through windows - had been increasing in frequency in recent months.
"They are really very frightened," she said. "The women, when they were talking to me yesterday, they were really upset, tears in their eyes and said, 'You know we love it here, we'd like to live here, but we're too scared.'
"A woman showed me her shoulder which was quite bruised and cut across, she was hit across the shoulder."
Jolena Flett, Racial Harassment Adviser for the Northern Ireland Council for Ethnic Minorities, said they had been threatened verbally and then three properties were attacked on the same day.
"There has been an issue about the families feeling unsafe in the properties they were attacked in. What we are trying to do is provide them with alternative accommodation," she said.
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