"אלו ואלו דברי א' חיים" vs "נעשית תורה כשתי תורות" with examples

Question

In numerous Halachic disputes I spotted two contradicting approaches:

1. "אלו ואלו דברי א' חיים" - both approaches are legitimate and stem from the [one] living G-d. Each one is allowed to keep his way and his Halochos without forcing others to accept.

2. "נעשית תורה כשתי תורות" - the two approaches appear as two different Torahs, therefore an obligating Halochoh must be issued for all.

How they can be reconciled?

(Understanding of this contradiction is especially useful for resolving my previous question about B"H and B"S wars: "what-happened-in-r-chananyas-penthouse-18-dvarim")

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Examples (I'm not claiming "שתי תורות applies in every example, but it looks like it):

1. B"H and B"S war: It was OK to have both schools side by side (as או"א) for some time, but [suddenly] it became "שתי תורות" and had to be [brutaly] resolved.

2. R' Yehoshua and R' Gamliel on Kiddush Hachodesh: it was fine to have different schools until R"G decided to end it and rule himself.

3. R' Eliezer and Chachamim in Tanuro Shel Achnai: R"E had his approach standing for decades alongside Chachamim's and all of sudden he finds himself boycotted.

Answer 1

In the book by Lampert "The Dynamics of Talmudic Dispute" he discusses the various approaches to "Eilu v'Eilu". I think you're misunderstanding when to apply Eilu v'Eilu. Not every dispute is an "Eilu v'Eilu" dispute. Lampert lists that Eilu v'Eilu is listed twice in the Gemara: Eiruvin 13b, Gittin 6b. Therefore it seems that it is only applied in those instances and not more generally, according to one view.

According to another view, Eilu v'Eilu applies to all Disagreements found in the Mishnah and Briasos. In tnis perspective then, the point is that both views are seen as valid, in of themselves. However, they're not valid halachically since halacha dictates that we follow one opinion.

In terms of the disagreements between Beis Hillel and Beis Shammai, again, you can't follow both schools simultaneously. As an example, you can't light the same Chanukia and start with both 8 lights and one light simultaneously. Halachically, we make a decision. That doesn't make Shammai's position less valid, it just makes it practical.

As regards the disagreement between Rabban Gamliel and Rebbi Yehoshua the Gemara is highlighting a point, that even if Rebbi Yehoshua was right at some level, having two dates on which to celebrate Yom Kippur is just impossible to follow. It means having two calendars to follow. Again, in terms of practicality we don't allow two versions. Nonetheless, I don't think you can apply Eilu v'Eilu in this case. Rebbi Yehoshua believed he was right, but he was actually wrong. Rabban Gamliel's position and calculations was the correct view, regardless of what Rebbi Yehoshua thought.

The last case you'll have to provide a source that this is the case. Nonetheless, the halachic rule is that we follow the majority in terms of practical application. So in this case also, regardless of Rebbi Eliezer's position, however valid, the Chachamim's position is the halacha.