Is any part of the X.org software multithreaded?

$ ps -eLf
UID        PID  PPID   LWP  C NLWP STIME TTY          TIME CMD
root         1     0     1  0    1 19:25 ?        00:00:00 init [4]
...    
root      1699     1  1699  0    1 19:25 ?        00:00:00 /usr/bin/kdm
root      1701  1699  1701  8    2 19:25 tty10    00:13:10 /usr/bin/X :1 vt10 ...
root      1701  1699  1703  0    2 19:25 tty10    00:00:00 /usr/bin/X :1 vt10 ...
root      1706  1699  1706  0    1 19:25 ?        00:00:00 -:1
root      1707  1699  1707  0    2 19:25 tty9     00:00:02 /usr/bin/X :0 vt9 ...
root      1707  1699  1710  0    2 19:25 tty9     00:00:00 /usr/bin/X :0 vt9 ...
root      1713  1699  1713  0    1 19:25 ?        00:00:00 -:0
....

answers your question, I think.

Nevertheless, the question seems to be mixing several things together - multithreading isn't about not using fork()/exec(). Threads share the same address space and if you want to run a different process you certainly don't want it to have access to the same address space. And if you decided not to use external programs (especially in the shell that since you mention it), you'd have to code all the functionality again.

Multithreading isn't a cure for everything. It can mostly be a cure only for well parallelizable problems actually - check wiki page for a nice short overview. Making a program multithreaded doesn't make it better, in most cases it makes it worse due to the bugs in synchronization code (if present at all).

in E. S. Raymond's book the author quotes .

The X server, able to execute literally millions of ops/second, is not threaded; it uses a poll/select loop. Various efforts to make a multithreaded implementation have come to no good result. The costs of locking and unlocking get too high for something as performance-sensitive as graphics servers. -- Jim Gettys