There has been an interesting case in New Zealand before their Human Rights Review Tribunal which deals with alleged breaches of the New Zealand Human Rights Act 1993 which is an Anti-Discrimination Statute similar to the British Equality Act 2010. It could have some relevance if a similar case is brought in Britain
In the case of Gay and Lesbian Clergy Anti-Discrimination Society Inc v Bishop of Auckland  NZHRRT 36 the Claimant who wanted to study to be a Clergyman in the Anglican Church in New Zealand sought to enter a time of discernment during which his sense of call would be tested and a decision made by a bishop whether training for the ministry should begin. The Bishop of Auckland, refused to allow him to participate in the process of discernment because he was in an unmarried same-sex relationship and could not therefore be ordained into the ministry. The Claimant alleged that this constituted unlawful Discrimination contrary to the Human Rights Act 1993 alleging Discrimination on the basis of his Sexual Orientation.
The New Zealand Act makes it unlawful to Discriminate on the grounds of Sexual Orinentation but provides an exemption in s39 which says
39 Exceptions in relation to qualifying bodies
(1) Nothing in section 38 shall apply where the authorisation or qualification is needed for, or facilitates engagement in, a profession or calling for the purposes of an organised religion and is limited to one sex or to persons of that religious belief so as to comply with the doctrines or rules or established customs of that religion.
this provision is very similar to the exemptions given to religious organisations in Britain by Schedule 9 Part 1(2) of the Equality Act 2010 where exemptions are given
so as to comply with the doctrines of the religion..... so as to avoid conflicting with the strongly held religious convictions of a significant number of the religion's followers.
In the New Zealand case reference was made to the recently passed New Zealand Marriage (Definition of Marriage) Amendment Act 2013 which like the British Marriage (Same Sex Couples) Act 2013 changed the legal definition of Marriage so as to permit Marriage between Same-Sex couples. The Tribunal however held that this change did not affect the case before them nor did it assist the Claimant in his argument with the Anglican Church
19. The purpose of [ the Marriage (Definition of Marriage) Amendment Act 2013 ] was to amend the Marriage Act 1955 by clarifying that for the purpose of New Zealand secular law, a marriage is between two people regardless of their sex, sexual orientation, or gender identity. The Amendment Act did not amend the doctrine of any church, including in particular that of the Anglican Church, regarding the sacrament of marriage as conceived by that church
In the case the Bishop of Auckland gave evidence about the Christian doctrine on Marriage as understood in the Anglican [and indeed all mainstream Christian] Churches as being between a Man and a Woman and that sexual relationships could only be approved of within such a marriage; therefore the relationship that the Claimant was in was incompatible with the doctrines of the Church. He stated that the, admitted, fact that some Bishops had made ordination decisions inconsistent with the doctrines of the Anglican Church did not change the doctrine of the Church.
There was some "evidence" from activists disputing this view of Anglican Doctrine but the Tribunal refused to be drawn into this noting
[33.3] Only Archbishop Richardson and Bishop Bay can speak for the Anglican Church. They spoke not just as experts, but as spokespersons for the Church and their evidence must be accepted. The separation of church and state must be maintained. The Tribunal cannot determine what is at heart an ecclesiastical dispute.
Para 42 of the Judgment is also worth quoting in its entirety as a very fine analysis of the nature of Religious Liberty
 The right of religious communities to determine and administer their own internal religious affairs without interference from the state is referred to as religious group autonomy (or “church autonomy”, to use the traditional label). See Ahdar and Leigh op cit 374 where it is noted that the importance of religious group autonomy to any overall scheme of religious liberty has been described as “most important”, “critical”, and “exceptionally high”:
Religious group autonomy is the freedom asserted by religious communities as groups. This freedom is not merely a “compound” or “aggregation” of individual members’ freedoms; it is the right the group asserts to its own religious exercise, separate and distinct from the rights and interests of its members. If religious groups are merely a combination of individual interests, a means to enhance personal autonomy, then this implies that these groups “are presumptively entitled to constitutional protection only to the extent that they do, in fact, enhance individual liberty”. This in turn implies greater vulnerability to state intervention into the internal affairs of such groups since the focus would be on vindicating individuals and their interests, not the group and its interests. In our view, this characteristically liberal and atomistic way of viewing religious groups (an aggregation of individuals contingently linked by religious preferences) seriously undermines religious freedom.
Religion is seldom if ever solely an individual matter. While a lone individual may clearly follow his or her own unique chosen path in matters of belief, worship, and practice, the vast majority of human beings only find it meaningful to pursue their religious objectives together with other like-minded individuals. There is an ineradicable collective or communal dimension to religion. Organizations or associations are formed to give effect to this communal aspiration. An individual’s religious life is very much tied to and dependent upon the health of the religious community to which that believer belongs. It requires a religious “infrastructure”.
The Judgment is of a high standard and considers European, American and British Judgments relating to the nature of religious freedom. As with all cases it ultimately relies on its own facts and its own National Legislation but it will undoubtedly be a valuable persuasive precedent in any future cases brought in Britain which challenge employment or similar decisions made by Churches in particular decisions by Churches refusing to offer or participate in Same-Sex Marriage ceremonies.