In general, the two grades interact rather well but on some issues there may need a bit of arbitration. Here is how I wrote it in the book:
The inevitable result is the emergence of two main categories of chareidim – the [Rabbi] Shimonists and the [Rabbi] Yishmaelists. These two strains co-exist within every chareidi community and often within chareidi households. In most aspects, there are no substantial adverse effects to this phenomenon. The Yishmaelists admire the Shimonists for maintaining a higher standard and the Shimonists appreciate that the Yishmaelists are ‘doing their job’. Essentially, they carry out a teamwork program (in the spirit of the Yissachar – Zevulun partnership) as, typically, both groups gain from the achievements of the other.
Problems do arise when Rabbi Shimonist chareidim expect or demand other chareidim who may lean toward the Yishmaelist school of thought to maintain their stricter standards. These problems tend to flare up in relation to community issues which collectively affect all of the chareidim in a community and where a common policy must be adopted. Here, these two conflicting schools of thought make it difficult to determine a single policy to serve the entire spectrum. In some cases, a rift within the community is unavoidable. This occurs mostly within the education system as that is one crux of the initial debate – should young chareidim be educated exclusively toward the higher Shimonist standard or not? Does the presence of the Yishmaelists make those standards harder to achieve? On occasion this disparity comes to the fore in family relations, mostly between fathers and sons (though sometimes even between husbands and wives or in-laws), sometimes with tragic consequences. This issue demands further study which I hope to provide.
To rephrase the question: Is it justified for a “high class” chareidi educational establishment to except potential students who do not fully fit their preferred profile, or are they beholden to accept them?
Well, listen to the opinion of one of the finest arbitrators in the business, L’orach yamim v’shanim tovim.
In the ensuing video, two school officials from Beit Shemesh are consulting with the "Rosh Yeshiva" Harav Aharon Leib Shteinman, Shlit"a. It seems that a local Beit Shemesh man is on the verge of remarrying to a widow from Bnei Brak who has two sons. As they are looking to settle in Beit shemesh, they want to enroll the two boys in this particular Talmud Torah.
The officials of the TT somehow feel that this widow is too "open minded" for their tastes and are seeking the Rosh Yeshiva's approval to not
The Rosh Yeshiva will have none of it! And he says so in no uncertain terms.
Oh, and pardon the English.
(Note - For email recipients who do not get the embedded video, you may access it HERE)
Note - Although this video was just recently published on YouTube, I am told that this incident occurred over a year ago.