Sergianism? Why, it's the faithful following of Catholics and Orthodox (mostly on the US East Coast for some reason) who read my site!
Seriously, it refers to the compromise literally beaten out of the head of the Russian Orthodox Church in 1927. Metropolitan Sergius (Stragorodsky), who became patriarch of Moscow shortly before he died in the 1940s, after spending time in prison, issued a declaration pledging Church support for the new Soviet government - this is our homeland so the joys and sorrows of the USSR are our joys and sorrows, etc. Also, he ordered Russian Orthodox clergy abroad to pledge not to criticize the Soviet government. He was a beaten, broken man trying to insure survival of the Church of Russia, in Russia, but of course many (most?) Russian Orthodox bishops abroad didn't go along with this outrageous order. This perpetuated a three-way split of Russian Orthodox worldwide that partly continues to this day.
1. The Russian metropolia in America didn't obey the order and so there was a schism from the mother Church until 1970, when the Russian Church proclaimed its American metropolia completely independent; the latter was renamed the Orthodox Church in America.
2. The Temporary Higher Admistration of the Russian Orthodox Church Abroad had been formed by escaped Russian bishops in Yugoslavia in 1920 - after 1927 the Church of Russia declared them excommunicated (IIRC). This group is now based in New York and is better known as ROCOR - the Russian Orthodox Church Outside of Russia.
3. In western Europe the Russian metropolitan in Paris, serving congregations of escaped/exiled Russians, eventually ended up under the patriarch of Constantinople and is under him today.