I'm trying to understand the methodology and the dynamics of the Halachah and when the Gemmorah presents a Machlokes that is resolved generations later I arrive at the conclusions that there was no obligation/established Halacha on that topic at the time of the Machlokes.
In other words, at least up until the time of the Machlokes, each side kept his own [ways of] Halochos.
For example, the numerous Machlokos between R' Moshe and the Israeli Rabbis Z"L prove that those Halochos were not established and each side kept his own Halochos.
What Rabbinical sources support/refute my conclusion?
I intentionally don't claim "there was no established Halacha on this topic ever", I can accept the claim of Moses or later generations kept it all in unison, I only ask about the conclusion about the specific time of the Machlokes (probably inferring that it was all lost in between).