Firefox ignores outline and focus styles on select elements when using Tab

This is a known bug which has sparked several Stackoverflow discussions. From what I have read, Mozilla have deemed that CSS is the wrong place to handle this element behaviour, and have opted instead to handle it by other means. At this time the only solution is to either use tabindex="-1" or to set the element to display as something else, and restyle the look and feel of a droplist — but be warned, this opens a can of worms in itself.

If you do opt to do this, I have had success in the past with the following kludge:

select {
    appearance: normal;
        -webkit-appearance: none;
        -moz-appearance: radio-container; /* renders text within select, without arrow chrome */
}

Appearance tells the browser to display the element as something else, but this is inconsistent from vendor to vendor. appearance: normal; is the spec, whilst webkit replaces normal with none. -moz-appearance: radio-container; has been the only way I have found to display the text within the chosen select option, whilst removing the arrow chrome for a fully customised droplist. However, try experimenting with the available options until you find something that works and doesn't add the focus ring you wish to customise. Internet Explorer will require further kludge to bend the select to your needs. Entirely possible, but out of scope for this question and answer.

Another solution is to set outline: none and set a box-shadow. For example:

.my_elements:focus
{
    outline: none;
    box-shadow: 0 0 3px 0px red;
}

So far the only way I've found to overcome it is to set the tabindex='-1' (see fiddle) which, of course, takes the element completely out of the tab selection chain. That would not be good for user interface, and my guess is not exactly what you desire (I assume you want to keep tab accessibility but just do your own styling for highlighting).