The feral animals have been causing havoc in the town in Gloucestershire for a number of years as they become more confident in venturing outside the forest in search of food.
According Rev Mike Barnsley, parish priest at St John the Evangelist Church, the animals now regularly wander into the church graveyard and cause damage to graves.
He told the Forest newspaper: "It is very distressing for families but so far nothing we have done has managed to keep them out.
"We try to keep the gates closed at all times and we ask visitors to close the gates after them, but the boar always seems to manage to get in.
"We have contacted the council and the Forestry Commission, but it appears they don't want to know. We just don't know what the solution is."
The Forestry Commission have advised locals to install boar-proof fencing, recommending electric fences and barbed wire.
But local Councillor Tim Gwilliam said that the Forestry Commision needs to take more responsibility for the animals.
He told the Daily Mail: "It's just not good enough. While old people are forced to watch the graves of their loved ones being dug up by the boar, they are busy setting up another workshop to talk about [it].
"They don't want to know because opinion is so divided. It's very difficult bringing people with such extreme views together, but that doesn't mean they can just wash their hands of it."
The Forestry Commission reported that 1,562 wild boars live in the Forest of Dean. The animal became extinct in the wild in the UK almost 300 years ago but farmers illegally dumped 60 into the woodland in 2004. Since then, the breeding population has been thriving.