Can I hide native tabs at the top of Firefox?

To hide the native tabs, you'll have to add a new file called userChrome.css and the css property visibility: collapse.

To do this, in Firefox click on Click on Menu -> Help -> Troubleshooting Information or navigate to about:support in the address bar.

Under the Application Basics section, there will be a section called Profile Directory with a button to Open Directory.

In the Profile Directory create a new folder called chrome. In the chrome folder create or edit the file userChrome.css if it already exists.

The contents of userChrome.css should be the following.

/* hides the native tabs */
#TabsToolbar {
  visibility: collapse;
}

Some optional further modifications to put in userChrome.css are:

/* hides the title bar */
#titlebar {
  visibility: collapse;
}

/* hides the sidebar */
#sidebar-header {
  visibility: collapse !important;
} 

A configuration that Xilin Sun uses is:

/* hides the native tabs */
#TabsToolbar {
  visibility: collapse;
}
/* leaves space for the window buttons */
#nav-bar {
    margin-top: -8px;
    margin-right: 74px;
    margin-bottom: -4px;
}

Try these out and see what you think looks best.

To answer your question in the comment, you may like this option better. I tried using visibility, but it was extremely flashy and jittery with the hover.

/* Option 1 */
#TabsToolbar {
    opacity: 0.0;
}

#TabsToolbar:hover {
    opacity: 1.0;
}

/* Option 2 */
#TabsToolbar {
    visibility: collapse;
}

#navigator-toolbox:hover #TabsToolbar {
    visibility: visible;
}

If you're running Windows 10, I've found the following gives the best integration:

1. Enable "Title Bar" mode by going to the hamburger menu (☰) → Customize → Check the "Title Bar" checkbox at the bottom of the screen.
2. Apply the following userChrome.css:

#main-window[tabsintitlebar="true"]:not([extradragspace="true"]) #TabsToolbar {
    opacity: 0;
    pointer-events: none;
}

#main-window:not([tabsintitlebar="true"]) #TabsToolbar {
    visibility: collapse !important;
}