A pastor must give permission for outside priests to offer Mass in his parish. Most pastors have no problem with allowing a bereaved family to have an outside priest celebrate the funeral Mass for their loved one in their parish. Why a pastor might refuse such permission, I don't know. That is something a spokesperson for the family should respectfully ask of the pastor.
It is also the case that a Catholic might not be able to have a funeral Mass if there is not a priest available to celebrate the funeral Mass. If no priest is available, then a deacon presides at a funeral liturgy outside of Mass. If neither priest nor deacon is available, then a trained and delegated layperson may preside at a funeral liturgy outside of Mass. (But, in such a situation, it would be all the more strange for a pastor not to welcome the possibility that an outside priest could offer a funeral Mass.)
As for refusing a funeral altogether, a pastor cannot deny a Catholic in good standing from being given a Catholic funeral and burial. It may be that the church is unavailable for the funeral from some extraordinary reason, in which case the funeral should be allowed to take place elsewhere, but ordinarily a Catholic has a right to a Catholic funeral and burial. If necessary, the local ordinary and/or the
St. Joseph Foundation should be approached for further assistance.
Can a pastor disallow another priest from offering a funeral Mass?
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