[css] I do not want to inherit the child opacity from the parent in CSS

If you have to use an image as the transparent background, you might be able to work around it using a pseudo element:

html

<div class="wrap"> 
   <p>I have 100% opacity</p>  
</div>

css

.wrap, .wrap > * {
  position: relative;
}
.wrap:before {
  content: " ";
  opacity: 0.2;
  background: url("http://placehold.it/100x100/FF0000") repeat;     
  position: absolute;
  width: 100%;
  height: 100%;
}