Bloomberg and Rudy ran as republicans. That did not make them conservatives. Maybe on one issue, they will have a conservative view point. But like Arnold, they are probably not conservative at all. And the city government is so liberal a true conservative will get nothing done. They will attack him and slow roll him so that he gets nothing done. But everything that happens will be his fault.
Bloomberg and Rudy ran as republicans. That did not make them conservatives.
https://kirkcenter.org/conservatism/ten-conservative-principles/