In the latest snapshop of the github code it seems the new function
Serial.setDebugOutput(0)
to turn off debug output is not working.

Usage:

 Serial.begin(115200);
 Serial.setDebugOutput(0);
 delay(10);

I traced the problem down to setDebugOutput() in HardwareSerial.cpp where there is a an if statement

if(uart_get_debug() == _uart_nr) {
            uart_set_debug(UART_NO);
}

that will fail to do its thing because uart_get_debug() (s_uart_debug_nr) will never be _uart_nr IF the function uart_set_debug() is never called with that value.
All places that uart_set_debug() is called are inside IF statements that wont run, kind of like a catch-22 situation.

Temp Solution
The temporary solution is to run a function that will set s_uart_debug_nr to something that will satisfy the IF statement above:

Serial.setDebugOutput(1); //sets s_uart_debug_nr to _uart->uart_nr

We can then turn it off,

Serial.setDebugOutput(0);

And it will properly be turned off.

 Serial.begin(115200);
  Serial.setDebugOutput(1);
  Serial.setDebugOutput(0);
  delay(10);

Semi permanent solution
A fix that works in the code comment out the inner IF inside setDebugOutput() as such:

//if(uart_get_debug() == _uart_nr) {
            uart_set_debug(UART_NO);
//}

However that may not make the function do whats intended.

True problem
The true problem is that the code inside uart_set_debug() is never run to initialize the settings that function does. Possibly run this function on .begin() to set things to a known state?
Something like:

void ICACHE_FLASH_ATTR HardwareSerial::begin(unsigned long baud, byte config) {
    uart_set_debug(uart_get_debug());  //new line

    // disable debug for this interface
    if(uart_get_debug() == _uart_nr) {

Another possible solution/error
Or possibly that last line in begin() is a typo and should be

void ICACHE_FLASH_ATTR HardwareSerial::begin(unsigned long baud, byte config) {
    // disable debug for this interface
    if(uart_get_debug() == UART_NO) {

Any one of these will fix the problem, it comes down to what is the intended sequence of the code. I hope this helps get it fixed and helps others.