Simplified if return suggestion from Android Studio
I prefer your method, because it's a lot clearer. But I would turn the if around (first check the input, then the normal action):

private boolean isTheParticipantTalking(ParticipantID participantId){
    if(mCurrentParticipant == null) {
        return false; // no one is talking
    }
    return participantId.equals(mCurrentParticipant.getId());    
}


Another question is if this is actually the best approach. 

Is a non-existing participant talking? That question really doesn't make so much sense. 

You could use Objects.requireNonNull which seems to have been written exactly for cases like this, or throw your own NullPointerException if you want to.