Even when the Bais Hamikdosh stood, the avoda was not always done k’halacha. There were extended periods of time where the Cohen Gadol was a Tzeduki or someone who bribed their way into the position. Additionally, halacha can change. A later Sanhedrin can override an earlier Sanhedrin.
In short, most of these machlokesim are not what did happen in the Bais Hamikdosh but what SHOULD happen in the Bais Hamikdosh.