One member of staff at the charity, who wanted to remain anonymous, said the abuse their colleagues had received in recent days had made them feel “physically sick”.
“There is a strong possibility it will directly affect the lives of the babies, children and vulnerable women I work with, some of whom have already been victims of hate crime in the UK,” they said.
“It makes me feel physically sick to hear that my colleagues have been abused online and had their lives threatened because of these actions.”
Another colleague said they felt “disheartened” by some of the messages they had received.
“It undermines the hard work we do to help others start new lives and feel safe in Wales,” they said.
“I was particularly discouraged by the wave of racist comments targeting staff.
“Wales welcomed us with open arms, providing the safety we were searching for.”