Does existence of a Machlokes prove the lack of established Halachah?

Question

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?

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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).

Answer 1

I can see three Rabbinical sources to support your point (Eruvin 6b):

הָרוֹצֶה לַעֲשׂוֹת כְּדִבְרֵי בֵּית שַׁמַּאי עוֹשֶׂה, כְּדִבְרֵי בֵּית הִלֵּל עוֹשֶׂה
but one who wishes to act in accordance with the opinion of Beit Shammai may do so, and one who wishes to act in accordance with the opinion of Beit Hillel may do so

And for later Tannaim (Chullin 116a):

תניא נמי הכי במקומו של רבי אליעזר היו כורתין עצים לעשות פחמין לעשות ברזל במקומו של רבי יוסי הגלילי היו אוכלין בשר עוף בחלב
In the locale of Rabbi Eliezer, where his ruling was followed, they would cut down trees on Shabbat to prepare charcoal from them with which to light a fire to fashion iron tools with which to circumcise a child on Shabbat. In Rabbi Eliezer’s opinion, not only does the mitzva of circumcision override Shabbat, but also any action required for the preparation of the tools necessary for the circumcision likewise overrides Shabbat. The baraita adds: In the locale of Rabbi Yosei HaGelili they would eat bird meat cooked in milk.

Also for Amoraim (Eruvin 94b):

וְרַב, אִי סְבִירָא לֵיהּ דַּאֲסִיר — לֵימָא לֵיהּ! אַתְרֵיהּ דִּשְׁמוּאֵל הֲוָה.
The Gemara asks: And Rav, if he maintains that in this case carrying is prohibited, he should have said so to him explicitly. The Gemara answers: It was Shmuel’s place. Rav did not want to disagree with his colleague in his jurisdiction, as he accepted the opinion of the local authority.