They cannot wait to throw up a "your browser is no longer supported :(" page for all Firefox users, and when that happens it will be over for our fox friend.
Whenever you see a site that does this, or a site that works on Chrome but not Firefox, report it at webcompat.com. Doing that will create an issue in github.com/webcompat/web-bugs.
For sites that are intentionally blocking Firefox users, Mozilla adds interventions or user agent overrides for those specific pages or scripts (go to about:compat in Firefox to see a list of them) to make it work with Firefox, even on sites trying to block Firefox.