It is well-established in the sunnah that the prophet encouraged his followers to keep their beards long, but trim their mustaches. It is also well-established in the sunnah that the prophet discouraged his followers from doing anything to resemble non-muslims.
It can even be said that the two are correlated, such that the command to keep the beard and trim the mustache is to directly oppose the practice of the pagans at the time (who, as I understand, would keep their mustaches long and trim their beards). The following hadith (Bukhari 7:72:780) suggests this interpretation, where the prophet is reported to have said:
Do the opposite of what the pagans do. Keep the beards and cut the mustaches short.
However, it is less clear exactly what the sunnah would be in a situation where the non-muslims also follow the practice of keeping their beards long while trimming their mustaches. Two examples would be the Hutterites, prevalent in the Canadian Prarires, or the Amish, prevalent in the Northeastern USA. Both of these groups are Trinitarian Christians, and as such neither are communities that we as Muslims should wish to emulate.
Even if one is not actually living in a Hutterite or an Amish community, the correlation between "long beard" and "Hutterite/Amish" is strong enough that a Muslim — especially a non-Arab Muslim — may be confused for one on sight.
In such situations, which would be the preferred tradition of the prophet to follow? Keep the beard and trim the mustache, or avoid resembling the non-muslims?