How much work can the unconstitutional conditions analysis do?

Regarding Steve's response, if a state where the death penalty is legal looked to hire an executioner, would an applicant who is conscientiously opposed to the death penalty have a legitimate claim to that job?  Requiring the waiver of the applicant's freedom of conscience wouldn't be an unconstitutional condition in that scenario, would it?  The object of the applicant's conscience claim is too wrapped up with the central duties of the job.  Maybe the unconstitutional condition analysis would work with Louisiana justices of the peace, who (I think) have a fairly broad set of responsibilities, but what about Massachusetts, where (I think) justices of the peace are primarily charged with performing marriages? Isn't the justice of the peace applicant who refuses to perform same-sex marriages a lot closer to the state executioner applicant who refuses to participate in the death penalty?