Looking through the code, it appears you can change the behavior by writing your own callback function for the av_log
function.
From the description of this function in libavutil/log.h:
Send the specified message to the log if the level is less than or equal
to the current av_log_level. By default, all logging messages are sent to
stderr. This behavior can be altered by setting a different av_vlog callback
function.
The API provides a function that will allow you to define your own callback:
void av_log_set_callback(void (*)(void*, int, const char*, va_list));
In your case, you could write a simple callback function that discards the messages altogether (or redirects them to a dedicated log, etc.) without tainting your stderr
stream.