In the UK ...

Now that marriage equality is the law in the UK, and given that the Church if England has come out against it, the issue of gay clergy themselves marrying and the question of blacklisting of said clergy has come up ...

Second priest defies Church of England to marry his same sex partner - Andrew Brown

[...] What will be hard for both men – and for any other clergy whose same sex marriages become public – will be to find another job. The archbishops have asked the bishop of Norwich, Graham James, to be available to diocesan bishops seeking advice on individual cases.

Priests in training or vicars who hold their jobs on time-limited contracts – as opposed to the older system of freehold which protects Andrew Cain – are much more vulnerable. They can be dismissed or their contracts dropped without obvious redress. Clergy are free to enter into civil partnerships, with the official justification that these need not involve sexual relations, which the church officially condemns outside of heterosexual marriage.

The wrangling over homosexuality has continued without progress for 30 years ...

You can read more about this at Thinking Anglicans - Bishop of Norwich's "blacklist" - which has comments to the post by Andrew Brown and Giles Fraser.