Change SVG fill color in :before or :after CSS

The accepted answer is incorrect, this is actually possible by applying a workaround with an SVG mask and background-color:

p:after {
  width: 48px;
  height: 48px;
  display: inline-block;
  content: '';
  -webkit-mask: url(https://gh.max.ax/heart.svg) no-repeat 50% 50%;
  mask: url(https://gh.max.ax/heart.svg) no-repeat 50% 50%;
  -webkit-mask-size: cover;
  mask-size: cover;
}

.red:after {
  background-color: red;
}

.green:after {
  background-color: green;
}

.blue:after {
  background-color: blue;
}

<p class="red">red heart</p>
<p class="green">green heart</p>
<p class="blue">blue heart</p>

You're not actually modifying the SVG DOM itself, you're just changing the background color. That way, you could even use images or gradients as background.

Update

As MisterJ mentioned, this feature is sadly not widely supported.

After six years, the support for prefixed use has risen to 97%.

Using the content property generates (non-exposed) markup functionally equvialent to an svg in an <img> element.

You cannot apply style to elements inside the svg document because:

1. styles are not allowed to cascade across documents
2. when using <img> (or content, or any css image property that references svg) the svg document is not exposed by the browsers due to security concerns

Similar questions, but for background-image here and here.

So, to do what you want you must get around the two points above somehow. There are various options for doing that, e.g using inline svg, using filters (applied to the <img>) or generating different svg files (or data URIs), as in your question.