[Avodah] nusach in shul

[Eli Turkel]

<<I have been in many shuls in EY where there is no set nusach. Instead,
the nusach goes by whomever is shaliach tzibbur.
So you will often have the circumstance where on Shabbat shacharit
is done in one nusach and Mussaf is done in the other.

...the appropriateness (or lack thereof) of having a shul with no set
nusach >>

Most poskim object to such a setup. Nevertheless it is very popular
in EY for practical reasons.
The simplest case is where there is a minyan at work. The participants
include ashkenaz, sefard (chassidic), sefardi, temani etc.
To start making separate minyanim for each group is in most cases
impractical or impossible. Thus, the standard practice is that the
nusach follows whoever is chazzan. Since, the participants can change
every day it makes no sense to go according to the majority and
it would also cause strife.

In "regular" shuls this mostly happens in smaller communities.
The shul is split between ashkenazi and sefard (chassidic).
For many reasons the shul and the rabbi does not want to split the
minyan even when it is possible, mainly for reasons of unity.
The possiblity of choosing one or the other would leave a very bad
taste. So the compromize is to let the chazzan choose even between
schararit and musaf. Note that when possible sefard (edot mizrach)
and temani frequently do set up a separate minyan for shabbat

-- 
Eli Turkel