To put not too sharp a point on the peel, they're having a hard time.
1. The community cannot raise the funds for a brick oven.
2. The local government/regulators/planning boards make permitting a wood-fired brick oven difficult.
Number one: Medium to large brick ovens can cost $20-50K. That is a significant sum. In the best of times, local food and farm groups have had difficulties attracting sponsors with deep enough pockets to fund a project like this. I can't help with this except to suggest attracting sponsors through their interest in the traditions of brick ovens.
In a relatively small geographic area, such as a neighborhood or semi-rural town, the use-cost ratio makes an oven difficult to justify. Expanding the project to include 'visiting' communities to use the oven can assist in both fundraising and community-building.
I have suggested in the past, that a mobile community oven would permit transport of the oven to different communities in a given radius from the home location. This also solves the problem of an investor/sponsor stipulating that if the group desiring the oven disperses, the ownership of the oven would default to the sponsor.
Mobile brick ovens do not need to look like the commercial mass-produced ovens available online. Customized designs that use traditional materials such as stone veneer or brick coupled with some innovative concealment of the trailer can make a mobile oven appear permanent.
Number two: Local codes permit fireplaces, wood stoves, pellet stoves, and conventional furnaces but have not always caught up with brick oven specs. In one location in southern CA, the local permitting person saw a brick oven as the same as a chiminea and said, 'no permit required'.
On the other hand, the following excerpt of an email came from a group in Minneapolis, MN attempting to build a community brick oven.
'The "Development Office" for the city, which handles zoning, has taken the position what it will prohibit outside wood-fire ovens anywhere in the city. They took one look at it and decided that because there is "fire" that makes an oven inherently dangerous. That, despite the fact that city parks have open grills that anyone can walk up to and build any kind of fire he or she wants to.'
Local codes may change the permitted height of the chimney, as with outdoor wood furnaces, but if it is possible for a code person to see a brick oven in use somewhere else, they may make a provision for a community oven.
OR let it be treated as a fireplace and go with codes governing that device.
Remember also, that local officials have different takes on what 'community' means. Despite a quantum leap in the maturity and wisdom of community groups since the 70's, there may be a lingering distrust of organized collections of community-minded people.