Belated Chanukah Drush

The Talmud Shabbat 21b states:

ת"ר מצות חנוכה נר איש וביתו 

והמהדרין נר לכל אחד ואחד 

והמהדרין מן המהדרין ב"ש אומרים יום ראשון מדליק שמנה מכאן ואילך פוחת והולך וב"ה אומרים יום ראשון מדליק אחת מכאן ואילך מוסיף והולך 

אמר עולא פליגי בה תרי אמוראי במערבא ר' יוסי בר אבין ור' יוסי בר זבידא חד אמר טעמא דב"ש כנגד ימים הנכנסין וטעמא דב"ה כנגד ימים היוצאין וחד אמר טעמא דב"ש כנגד פרי החג וטעמא דבית הלל דמעלין בקדש ואין מורידין 

אמר רבה בר בר חנה א"ר יוחנן שני זקנים היו בצידן אחד עשה כב"ש ואחד עשה כדברי ב"ה זה נותן טעם לדבריו כנגד פרי החג וזה נותן טעם לדבריו דמעלין בקדש ואין מורידין

Our Rabbis taught: The mitzvah of Hanukkah is one light for a man and his household; 

The mehadrin is a light for each member [of the household]. 

The mehadrin of the mehadrin — Bet Shammai maintain: On the first day eight lights are lit and thereafter they are gradually reduced;  but Bet Hillel say: On the first day one is lit and thereafter they are progressively increased. 

Ulla said: In the West [Palestine] two amoraim,  R. Jose b. Abin and R. Jose b. Zebida, differ therein: one maintains, The reason of Bet Shammai is that it shall correspond to the days still to come, and that of Bet Hillel is that it shall correspond to the days that are gone; but another maintains: Bet Shammai's reason is that it shall correspond to the bulls of the Festival; whilst Bet Hillel's reason is that we rise in sanctity but do not go down. 

Rabbah b. Bar Hana said: There were two old men in Sidon: one did as Bet Shammai and the other as Bet Hillel: the former gave the reason of his action that it should correspond to the bulls of the Festival, while the latter stated his reason because we rise in sanctity but do not go down.

What does it mean to have mehadrin? What does it mean to have an argument over what mehadrin min hamehadrin is, Bet Shammai and Bet Hillel? What is the meaning of an argument over what their reasons for their argument were? Lastly, what is the purpose of two elders in Tzidan, each holding either of Bet Shammai, or of Bet Hillel, and agreeing with the reason of one of the other machlokot over the other reason? Especially in light of the Rif and others who do not pasken one way or another, is this to show that both reasonings are valid, both Bet Shammai and Bet Hillel are valid?

We must realize the incredible statement in the last story. Two people in the same town, one did like Bet Shammai, one did like Bet Hillel. In this particular instance, they actually negate each other. Think about it. If someone was coming from a desert island to Tzidan and tried to figure out what day it was based on the number of candles, he would be unable. On the first day, one would have 8 and the other 1. The third, 3 and 6. The fifth, 5 and 4. Never the twain shall meet, Bet Shammai and Bet Hillel will never have a day that agrees. The eight days of the holiday ensure this. According at least to Tosafot, the whole point of the mehadrin min hamehadrin is so people will know the day, and in this town, it would have been impossible.

We learn, homiletically, that true mehadrin min hamehadrin is the ability to differ about the aesthetics of Judaism, what we find symbolic and "extra-halachic", and still coexist in the same town. The mehadrin is the ability to have machloket and live together. Each offers different reasonings, and each completely disagree, to the point where their mitzvit actually negate the other, yet they could live together, as two elders, leaders, in one town.

How can this be done?

We should note that it is particularly within the arguments of Bet Shammai and Bet Hillel where we find this great ability to coexist even when arguing. The Mishna Yevamot 1:4 states that although Bet Shammai and Bet Hillel disagreed over the validity of certain marriages, they continued to intermarry between schools:

אף על פי שאלו [ אוסרין ואלו מתירין, אלו ] פוסלין ואלו מכשירין, לא נמנעו בית שמאי מלשא נשים מבית הלל, ולא בית הלל מבית שמאי.כל הטהרות והטמאות שהיו אלו מטהרין ואלו מטמאין, לא נמנעו עושין טהרות אלו על גבי אלו.

Even though these [one school] prohibit and these [the other school] permit, these disqualify and these allow, Bet Shammai did not refrain from marrying women from Bet Hillel, nor did Bet Hillel [refrain from marrying women] from Bet Shammai. [With regard to] purity and impurity where these ruled [a matter] pure and these ruled [it] impure, they did not refrain from using [utensils] the other deemed pure.

Now, this statement has many explanations, for how could Bet Shammai or Bet Hillel ignore their halachic psak and allow their sons and daughters to marry possibly illegitimate stock?

The Talmud (Yevamot 14a) is also concerned for this question. One answer is that if the psak was like Hillel after voting, then Bet Shammai would hold like that. But what about the opinion that they continued to hold their own psak even in the face of the vote? The Talmud declares that the meaning of the Mishna is that when there were possible issues according to Bet Shammai, Bet Hillel would inform them, and vice versa.

We see the secret, then, to keeping peace to arguing sides of Judaism's legacy, is the ability to be cognizant, and more, respectful, of the other sides and their views. It doesn't necessarily require legitimization to do this. If this can be done within legitimate views of halacha, all the more so when it comes to our mehadrins, the little things that give us more flavor and color within Judaism. We can be respectful, even when we don't accept the other's opinion. Disagree, without being disagreeable. Unite in difference, unite in deference.