Shul segregation during chol hamoed

Question

Over Pesach and Sukkos, it is common to find segregated minyanim in which those who wear tefilin sit in one section while those who do not sit in another, or completely separate services for both. Where does this practice originate, and why would segregation trump other seating concerns like makom kavuah?

Additionally, in discussing this issue with someone, he brought up an instance in which there were 9 people of one minhag who disbanded the minyan rather than count someone as the tenth since they were of the opposite minhag. This seems... problematic. For one, they seem to be deliberately precluding people from being in the tzibbur, potentially violating inyanim of poreish tzibbur and lo tisgodedu (this is less of a halacha and more of a drash...) Secondly they are potentially abandoning the opportunity for tefilah betzibbur for a minhag (to be clear, I'm referring to separation between practitioners and discounting those of different practice). Thirdly, they wouldn't discriminate in this way if the tenth was someone who just didn't have tefilin with him, so why is this different?

To summarize:

Why is the issue of tefilin on chol hamoed taken so seriously as to require segregation, discrimination, and apparent violation of other minhagim and halachos?

Answer 1

According to the OU regarding tefillin on chol hamoed:

We should take care that we don’t have a situation where some in the congregation are wearing tefillin and others are not as this is considered divisive.

They are basing this statement on Mishneh Brurah 31:8

דאין נכון שבהכ"נ אחת קצתם יניחו תפילין וקצתם לא יניחו משום לא תתגודדו. ומי שאין מניח תפילין בחוה"מ שמתפלל בבה"מ שמניחין תפילין יש לו ג"כ להניחן ובלי ברכה וצבור שנהגו להניח תפילין אין להם לשנות מנהגם:‏

It is not correct that in one synagogue, some people should put on tefillin and some should not due to (the prohibition of) "lo titgodedu". Someone who does not put on tefillin normally on chol hamoed who is praying in a synagogue where they do put on tefillin should do so as well without a berakha...

^{my translation}

Though the MB doesn't explicitly mention this case, my rabbi also told me that if I'm ever davening in a minyan where people don't put on tefillin, I should not do so in shul either but rather wait until I get home.

Regarding your first two points, the synagogue isn't preventing tefila betzibur; the people who leave rather than adapt to the custom of the shul are.

Regarding your third question, I don't have a solid answer. My guess would be that since tefillin on chol hamoed is known to be a divisive issue, someone not wearing tefillin on those days is more likely to be understood to be making a political statement than someone without tefillin on a regular day.