CSS - How to Style a Selected Radio Buttons Label?

You are using an adjacent sibling selector (+) when the elements are not siblings. The label is the parent of the input, not it's sibling.

CSS has no way to select an element based on it's descendents (nor anything that follows it).

You'll need to look to JavaScript to solve this.

Alternatively, rearrange your markup:

<input id="foo"><label for="foo">…</label>

If you really want to put the checkboxes inside the label, try adding an extra span tag, eg.

HTML

<div class="radio-toolbar">
 <label><input type="radio" value="all" checked><span>All</span></label>
 <label><input type="radio" value="false"><span>Open</span></label>
 <label><input type="radio" value="true"><span>Archived</span></label>
</div>

CSS

.radio-toolbar input[type="radio"]:checked ~ * { 
    background:pink !important;
}

That will set the backgrounds for all siblings of the selected radio button.

.radio-toolbar input[type="radio"] {
  display: none;
}

.radio-toolbar label {
  display: inline-block;
  background-color: #ddd;
  padding: 4px 11px;
  font-family: Arial;
  font-size: 16px;
  cursor: pointer;
}

.radio-toolbar input[type="radio"]:checked+label {
  background-color: #bbb;
}

<div class="radio-toolbar">
  <input type="radio" id="radio1" name="radios" value="all" checked>
  <label for="radio1">All</label>

  <input type="radio" id="radio2" name="radios" value="false">
  <label for="radio2">Open</label>

  <input type="radio" id="radio3" name="radios" value="true">
  <label for="radio3">Archived</label>
</div>

First of all, you probably want to add the name attribute on the radio buttons. Otherwise, they are not part of the same group, and multiple radio buttons can be checked.

Also, since I placed the labels as siblings (of the radio buttons), I had to use the id and for attributes to associate them together.