BBC News understands the Glasgow centre made the decision to end its membership in February and has since had a number of meetings with RCS to discuss concerns.
Its view was it wanted to go beyond providing single-sex spaces and make the whole service women-only.
The Glasgow centre said the decision to end its membership with RCS was not taken lightly.
A spokesperson for its board said: “After careful consideration, we have concluded that the interests of our organisation, and those that rely on our services, will be best served and represented outwith membership of RCS.
“We were created to provide support by and for women. We believe, and women have consistently told us, that single-sex services delivered by an all-female workforce are crucial to help them heal from sexual trauma. This approach remains our priority but is at odds with RCS’.”
Under updated guidance, external from the Equality and Human Rights Commission, that was published earlier this year, the definition of women only can include trans women who have a gender recognition certificate (GRC).
However, it is legal to prevent trans women – including those with a GRC – from applying for a women-only role if it is a “proportionate means of achieving a legitimate aim”.
RCS, which is the national charity that sets service standards for member centres, said it wished the Glasgow team well and that it provided a crucial service for survivors.
A spokesperson added: “Our member centres deliver services in a variety of ways, tailored to the needs of the communities they serve.
“What is fundamental across all Rape Crisis Services is that survivors’ needs are at the centre of their provision.”
