Catholic school governors and leaders who are gay, remarry or live with a partner could face the sack or disciplinary action, according to new advice from the Church.
Guidance for Catholic schools, published last month, says there are "substantive life choices" which are incompatible with the Church's teachings.
Those who make such choices, who hold key positions in a school, could face an investigation and ultimately disciplinary action, or be removed from their post, it says.
Concerns have been raised that the booklet, Christ at the Centre, is placing tight restrictions on teachers' private lives.
The National Secular Society (NSS) said the lawful, private activities of teachers "should not be any business of prying employers".
It said it had written to education secretary Michael Gove asking for the document to be withdrawn.
Under current rules, head teachers, principals, deputy heads and heads of RE at Catholic schools are required to be practising Catholics. This also applies to the majority of a school's governing body.
People holding these key posts are required to conduct themselves in a way which does not conflict with the Church, the guidance says.
It says: "There are also substantive life choices which are incompatible with the teaching of the Catholic Church and which may be detrimental or prejudicial to the religious ethos and character of a Catholic school."
These could include:
- Getting married in a non-Catholic church, register office or other place without special dispensation
- Remarrying after divorce
- "Maintaining a partnership of intimacy with another person" outside of marriage approved by the Church "where this would, at least in the public forum, carry the presumption from their public behaviour of this being a non-chaste relationship"
- Publishing or distributing materials that are contrary to Gospel values and the teaching of the Catholic Church
The booklet says that if someone who has been appointed to a key school post makes a substantive life choice that is incompatible with Church teachings then "their ability to govern or to lead and model Catholic life and faith with ecclesial integrity may cease to exist".
This could lead to an investigation and in some circumstances "may necessitate a member of the governing authority of a Catholic school being removed from office or disciplinary action being taken against someone appointed to a key post".
NSS executive director Keith Porteous Wood said: "A growing percentage of teachers in Roman Catholic schools are not Catholics, and a significant proportion of Catholic teachers will have made life choices which are deemed incompatible with the teaching of the Catholic Church.
"However good they are as teachers, both groups have cause to sleep less easily as the Church becomes ever more intolerant of lifestyles that are becoming commonplace.
"The lawful private activity of teachers, particularly in publicly funded schools, should not be any business of prying employers."
He told the Times Educational Supplement: "The restrictions concerning the private lives of teachers employed in state schools go beyond the pale."
A spokeswoman for the Catholic Education Service told the magazine: "The recently revised document Christ at the Centre offers guidance to governing bodies, staff and parents about the ethos and values of Catholic schools.
"It is a matter for governing bodies and dioceses to make staffing decisions based on local situations."
The Catholic Education Service spokeswoman added: "The purpose of this guidance booklet is to unpack the expectations of those in, or who aspire to, leadership positions within Catholic schools."