Martine Delaney had complained to Tasmania's Anti-Discrimination Commission about a booklet produced by Australia's Catholic bishops.

The booklet, titled "Don't Mess with Marriage", was a pastoral letter from the bishops sparked by the same-sex marriage debate.

Ms Delaney and Hobart archdiocese agreed to enter conciliation last year, but the activist said the Church refused to budge from its position.

Ms Delaney said she withdrew her case to avoid a lengthy tribunal battle.

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