Do Catholics have to request a religious exception for matters of conscience from their parish priest?

There are numerous stories on the National Catholic Register about Bishops who have decided to [prohibit priests](https://www.ncregister.com/cna/monterey-bishop-prohibits-religious-exemption-from-covid-vaccine-mandates) in their dioceses from granting religious exceptions for Covid-19 vaccines. Is there any reason that an individual Catholic shouldn't seek a religious exemption from a member of the clergy who shares their concerns with the nature of the vaccines, even if is not their parish priest?