Is there a commonly supported way to make a skewed "frosted glass" effect in CSS/SVG?

You can consider skew transform without the need of clip-path. here is a basic example where the trick is to specify the correct value of background-position to create the illusion of one image.

.box {
  height:300px;
  background-image:url(https://picsum.photos/600/800?image=1069);
  background-position:left center;
  background-size:cover;
  position:relative;
  overflow:hidden;
}
.skew,
.skew::before{
  position:absolute;
  top:0;
  left:0;
  right:0;
  bottom:0;
  transform-origin:top left;
  transform:skewY(30deg);
  overflow:hidden;
  background-image:inherit;
  background-position:inherit;
  background-size:0 0;
}
.skew::before {
  content:"";
  transform:skewY(-30deg);
  filter:blur(10px);
  background-size:cover;
}

/*to illustrate the separation*/
.skew {
  border-top:1px solid;
}
/**/
.container {
  position:relative;
  z-index:1;
  margin-top:150px;
  padding-left:50px;
}

body {
 margin:0;
}
<div class="box">
  <div class="skew"></div>
  <div class="container">
    <h1>some text</h1>
    <p>Lorem ipsum</p>
  </div>
</div>

<div class="box" style="background-image:url(https://picsum.photos/600/800?image=3)">
  <div class="skew"></div>
  <div class="container">
    <h1>some text</h1>
    <p>Lorem ipsum</p>
  </div>
</div>

In case you want the skew to be responsive you can add a small JS code to adjust the angle and always cover half the iamge:

var w = window.innerWidth;
var h = 300; /*the height of the box*/
document.querySelector('.box .skew').style.transform="skewY("+(Math.atan(h/w)*180/Math.PI )+"deg)";
document.querySelector('.box .skew span').style.transform="skewY(-"+(Math.atan(h/w)*180/Math.PI )+"deg)";

window.onresize = function(event) {
    w = window.innerWidth;
    document.querySelector('.box .skew').style.transform="skewY("+(Math.atan(h/w)*180/Math.PI )+"deg)";
    document.querySelector('.box .skew span').style.transform="skewY(-"+(Math.atan(h/w)*180/Math.PI )+"deg)";
};
.box {
  height:300px;
  background-image:url(https://picsum.photos/600/800?image=1069);
  background-position:left center;
  background-size:cover;
  position:relative;
  overflow:hidden;
}
.skew,
.skew span{
  position:absolute;
  top:0;
  left:0;
  right:0;
  bottom:0;
  transform-origin:top left;
  transform:skewY(30deg);
  overflow:hidden;
  background-image:inherit;
  background-position:inherit;
  background-size:0 0;
}
.skew span{
  transform:skewY(-30deg);
  filter:blur(10px);
  background-size:cover;
}
/*to illustrate the separation*/
.skew {
  border-top:1px solid;
}
/**/
.container {
  position:relative;
  z-index:1;
  margin-top:150px;
  padding-left:50px;
}

body {
 margin:0;
}
<div class="box">
  <div class="skew"><span></span></div>
  <div class="container">
    <h1>some text</h1>
    <p>Lorem ipsum</p>
  </div>
</div>


You can also make it all in a single <svg> image, using a <pattern> element to fill half a triangle with the image, and apply your filter on it.

svg {
  width: 100vw;
  height: 200px;
  position: absolute;
  top: 0;
}

.container {
  position: relative;
  z-index: 1;
  margin-top: 100px;
  padding-left: 50px;
}
<svg width="1024" height="200" viewBox="0 0 1024 200" preserveAspectRatio="none">
  <defs>
    <pattern id="pat" viewBox="0 0 1024 200" width="100%" height="100%">
      <image xlink:href="https://picsum.photos/1024/200?image=1029" width="1024" height="200"/>
    </pattern>
    <filter id="blur">
      <feGaussianBlur in="SourceGraphic" stdDeviation="10" />
    </filter>
  </defs>
  <!-- background no filter -->
  <rect width="1024" height="200" fill="url(#pat)"/>
  <!-- foreground triangle, blurred -->
  <path d="M0,0L1024,200H0Z" fill="url(#pat)" filter="url(#blur)"/>
</svg>
<div class="container">
  <h1>some text</h1>
  <p>Lorem ipsum</p>
</div>

Tags:

Html

Css

Svg

Sass