In many places, members of all the different ethnic groups pray together. That is the accepted practice in many yeshivot, so as not to cause a daily schism between the students, as well as in small communities which do not have enough people for each group to maintain a large minyan to pray and learn Torah.
In the past, in order to refrain from disrupting the prayer service and creating separate minhagim within the same synagogue, the congregation would establish one nusach according to the majority (see Igrot Moshe, Orach Chaim, part 4, 34). However, in our society, where people are familiar with and accustomed to the different minhagim, in many places it is customary to give each ethnic group expression in the prayer service. Usually, the congregation follows the chazan. For example, if the chazan is Sephardic, he will pray in the Sephardic nusach, and if he is Ashkenazic, he will pray in the Ashkenazic nusach. There are places that even if the chazan is Yemenite, although his pronunciation varies greatly from the norm, he prays in his Yemenite dialect. Since all the minhagim are acceptable and known to all, there is no fear of “lo titgodedu,” and it is not likely to incite controversy.
That is how we practice in Har Berachah. When there are major differences between the minhagim, it is our custom to follow the shorter nusach. For example, on “Bet-Hei-Bet” (fast days enacted on Monday and Thursdays by some ashkenazic authorities), when the Ashkenazim customarily say Selichot, we do not recite them communally, since the Sephardim do not follow this custom. Similarly, Shir HaShirim (Song of Songs) is not recited before Kabbalat Shabbat, though it is the minhag of many Sephardim. Likewise, we do not recite all the passages of the Korbanot (sacrificial offerings) out loud in the minyan, as is the Sephardic tradition. Those who wish to say them recite them individually before the prayer service. However, when the extension to the prayer service is not burdensome, the congregation follows the chazan; for instance, at the end of the prayer service, when the Sephardim prolong the recital of the Psalm of the Day and the Pitum HaKetoret, or the Tachanun of Mondays and Thursdays.
The Sephardic minhag is that the chazan recites all the Psalms and Birkot Keriat Shema out loud, in order to fulfill the obligation for a person who does not know how to read. Nevertheless, the prevalent custom is that even the Sephardic chazanim say only the conclusion of the mizmorim and berachot out loud. This is because nowadays everyone knows how to read, and the recital aloud prolongs the duration of the prayer service and disrupts the kavanah of some of the people praying.
As a general rule, regarding prayers recited out loud, the congregation follows the chazan, while concerning prayers recited silently, each person prays according to his individual minhag. Nonetheless, it is unnecessary to be meticulous concerning this, and one who wishes to pray in the chazan’s nusach is permitted to do so, for that is the opinion of some poskim. One who wishes to pray in his own nusach, even those passages recited aloud, is permitted to do so, as long as he says them quietly, so as not to disturb the congregation and accentuate the differences between him and the chazan.
When the Sephardic chazan recites the Thirteen Attributes of Mercy three times in the prayers of supplication (tachanunim) of Mondays and Thursdays, it is proper that the Ashkenazim follow along with him.
To conclude, in all these situations, in which the benefit to the community and to the prayer service are weighed against the preservation of nusachim, the mara d’atra, the primary rabbi of the place, must determine what is best.