In order to make Firefox behave a certain way for all websites that you visit you have to either edit the default user style sheet or the Firefox config file.

Mac users: navigate to {user}/Library/Application Support/Firefox/Profiles/Chrome{your user profile}
PC users: navigate to C:\Program Files\Mozilla Firefox\defaults\profile\chrome

and open the file userContent-examples.css and add either one of the solutions into the CSS file and save as userContent.css
Disable the border:

a {
    outline: none;
}

Tidy up the border:

a {
    overflow: hidden;
}

There is also a way to get rid of the outline border by editing the Firefox config file (keep in mind this will remove the border completely)

1. Type “about:config” in Firefox’s location bar
2. Find the string: browser.display.focus_ring_width
3. Set the value to 0

Now Firefox will behave as you want across all websites you visit. Gotta love user based style sheets.