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%;
}