Q:

Ignoring StopAllAudio() in Unity3D

There is an AudioSource with background music. After a certain action, StopAllAudio is activated. I want the background music not to turn off, how to do?

A:

I'll just guess into the dark that you are using the StopAllAudio from this thread like
private AudioSource[] allAudioSources;

private void Awake() 
{
    allAudioSources = FindObjectsOfType<AudioSource>();
}

public void StopAllAudio() 
{
    foreach(var audioSource in allAudioSources) 
    {
        audioSource.Stop();
    }
}

So if you want to exclude a certain (or multiple) AudioSource from beeing stopped you could use
// configure this in the Inspector
// set the size and reference according AudioSource(s)
// e.g. your background music source
public List<AudioSource> doNotStopSources = new List<AudioSource>();

private AudioSource[] allAudioSources;

privtae void Awake() 
{
    allAudioSources = FindObjectsOfType<AudioSource>();
}

public void StopAllAudio() 
{
    foreach(var audioSource in allAudioSources) 
    {
        // ignore AudiioSource if it is in doNotStopSources
        if(doNotStopSources.Contains(audioSource)) continue;

        audioSource.Stop();
    }
}

