I went to my profile settings and added a folder called 'chrome' and a file called userChrome.css.
I included this code:
@namespace url("http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul"); /* only needed once */
#tabbrowser-tabs .tabbrowser-tab .tab-close-button { display:none!important; }
I restarted my Firefox instance and it still shows the X close button in the tabs.