I can't seem to figure out why Firefox is using the default svg fill color instead of the class's fill.

Here are the 3 fills when viewing the FF inspector:

CSS

SVG is being inserted via

<svg class="icon">
    <use xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="#menu-bag"></use>
</svg>

It should be showing the .skip-link .icon fill of white (#fff) but it's actually using the SVG fill of #002649; If i change .skip-link .icon to .skip-link svg then it works fine. Why can I not use a class and instead but explicitly state the element??

Am I missing something obvious about how Firefox fills an SVG? This CSS works fine in other browsers.

Robert is correct that <use> is not always applied consistently. Certainly when you use an SVG as an image, it doesn't know how to apply any of the CSS rules you've added to your page.

But there are a lot of other things here as well that could decide the element's style so an example might be helpful.

Here's a stack snippet to center our discussion.

<!-- begin snippet: js hide: false --> <!-- language: lang-css -->
svg {
  fill: blue;
}
a:hover svg {
  fill: red;
}
.skip-link .icon {
  fill: purple;
}

.green {
  fill: green;
}
<!-- language: lang-html -->
<a href="#" class="skip-link">
  <svg xmlns="http://www.w3.org/2000/svg"
       xmlns:xlink="http://www.w3.org/1999/xlink"
       class="icon" >

    <def>
      <text id="text" >use xlink</text>
      <text id="over" class="green">use xlink override</text>
    </def>
    
    <text x="5" y="15" >Plain</text>
    <use  x="5" y="30" xlink:href="#text" />

    <use  x="5" y="50" xlink:href="#over" />
    <text x="5" y="65" class="green" >class="green"</text>
    <text x="5" y="80" fill="orange" >fill="orange"</text>

  </svg>
</a>
<!-- end snippet -->

Specificity

The SVG element itself is being styled with several conflicting rules. What determines which rule wins has to do with [specificity and order]. In this case, the SVG element itself will end up purple. The hover anchor rule, for example, will never show up because it is less specific than .skip-link .icon

SVG

Inheritance

Some properties allow for inheritance from their parents, but only when not specified themselves. Any specifications will override the inherited value. If the question is, my <svg> element has a certain style, why isn't it being applied to all child elements equally, the answer is simple. It's perfectly fine for child elements to specify their own value and override the inherited one.

<text x="5" y="65" style="fill:green;" >class="green"</text>
<text x="5" y="80" fill="orange" >fill="orange"</text>

Use & Xlink

The tricky part becomes what happens when use is involved. In this case, it can be hard to trace the actual styles being applied. Use will create an inline representation of the element identified by the xlink attribute, but you cannot access this element directly. Therefore, selecting use in the developer tools will only reveal the styles applied to the parent of the element. The element itself may override the inherited properties and we'd have no way of observing it in the dev panel.

Here, for example, the style applied to use is inherited from the parent. In the developer tools, it appears that the winning rule is purple, but this is only because it hasn't taken into consideration the element being pulled in. This is a soft value that can be overridden if the element specifies any value.

use

But the full set of selectors for the inlined text would actually look like this:

text

Specific Situation

One thing I'd suggest in the future is providing runnable code that other people can use to easily reproduce the issue as it saves a lot of extra debugging time. However, here's what I suspect is happening with your exact situation:

<!-- begin snippet: js hide: false --> <!-- language: lang-css -->
svg {
  fill: #002649;
}
a:hover svg {
  fill: #8A8B8C;
}
.skip-link .icon {
  fill: #FFF;
}
<!-- language: lang-html -->
<a href="#" class="skip-link">
  <svg xmlns="http://www.w3.org/2000/svg"
       xmlns:xlink="http://www.w3.org/1999/xlink"
       class="icon" >

    <def>
      <svg xmlns="http://www.w3.org/2000/svg" id="menu-bag">
        <rect height="100" width="100" />
      </svg>
    </def>

    <use xlink:href="#menu-bag" />

  </svg>
</a>
<!-- end snippet -->