The letter, addressed to Mark Drakeford, the First Minister of Wales, said: "In seeking to enforce so-called 'neutral values' curriculum, which we would argue is impractical and undesirable for today's Welsh society, the risk is that the government is moving towards a homogeneous education system which will no longer recognize the importance of allowing children to pursue a deep knowledge and spiritual understanding of faith."
It added: "We would seek your reassurance that it is not the government's intention to damage the distinctive Catholic nature of our schools."
The CES submission also warned the government that it risked undermining the role of parents as primary educators of their children if it removed parents' right to withdraw their children from both RE and Relationship and Sex Education.
It said: "The removal the right of withdrawal is an erosion of parental rights and represents a regressive step in the trust and relationship between parents and the state, and parents and schools."
The CES also expressed concern that the proposal could pave the way for future infringements of religious freedom.
It said that a clause in the new bill "means that the Welsh government could specify content and teaching of Catholic RE for pupils above the age of 14. The Welsh government could require pupils in Catholic schools to engage in courses of study which do not meet the requirements of the denominational religious authority (in our case the diocesan bishop)."
"The Welsh government will be able to introduce these requirements by regulation, which means that the changes would be made without the opportunity for appropriate scrutiny and opportunity for challenge."