In accordance with the Rutan decision, and even without it, as mayor, I would not deny any potential employee an opportunity for employment based on their party affiliation.
One of the reasons I do not favor privatization of public assets and responsibilities, is precisely because privatizing goods and services increases the potential to avoid the appropriate monitoring and scrutiny that a public entity undergoes. This is particularly true if the public loses control of those assets. Nonetheless, a contract with a private entity can be structured so as to build in the public scrutiny and oversight, including those related to hiring.
This has been a concern of mine for years and will work to put new rules into place.