The Bishop of Menevia, the Right Reverend Thomas Burns, wants to demolish St Winefride’s in Aberystwyth on safety grounds.
There are plans to build a new church outside the town centre with the sale proceeds.
But an objector said some parishioners do not want to move out.
Our Lady of the Angels and St Winefride’s was built in the 1870s and is said to have a congregation of about 150 for its Sunday morning service.
In a pastoral message, Bishop Burns, who is based in Swansea, said the church was not fit for purpose and could be closed on health and safety grounds.
Plans are to demolish St Winefride’s and sell the land for housing.
He said: “My dear people, the above tactics that the protesters have used, including petitions and submissions to their local councillors, have brought us to a serious moment. Throughout these last few years, the structure of St Winefride’s church has continued to weaken. It is in such a bad state that our insurers can no longer provide suitable cover for the deteriorating walls and roof if they should collapse. I am increasingly concerned about health and safety matters. Masonry and other bits and pieces have been coming down. I may soon have to make a decision about closing the church, to prevent risks to life and limb.”
The church site in Queen’s Road, which includes a dilapidated parish hall and presbytery, would cost the diocese more than £2.6m renovate, added the bishop.
But objectors claimed they had been shown no evidence the church was structurally unsound.
Appealing to his parishioners, Bishop Burns added: “Tell the protesters politely to back off. Speak to them, or write to them. You know who they are, and you also know that they do not represent your parish. They have contributed to the heavy costs that have already been incurred, amounting to over £100,000. Please tell them that enough is enough. They risk leaving Aberystwyth with no Catholic parish church at all.”
But the bishop said church services would be tailored to bus schedules, where possible.
An objector to plans for St Winefride’s, who wished to remain anonymous, said: “The old church (St Winefride’s), which has been there since the 1870s, is planned to be demolished because they say it’s not fit for purpose. Some parishioners go along with this and others do not. We don’t want the church to move out of the town centre.”
The objector also questioned whether the church was structurally unsound although agreed it was in need of repair.