As reported on Phoronix a few times, the GTK3 port of Firefox is still being worked on along with the Wayland port. The GTK3 version of Firefox hasn't yet hit the mainline code-base, but progress is being made and for allowing Firefox/Gecko to avoid its hard dependencies on X11 interfaces.
While there's still some work to go, Frederic Plourde of Collabora has reminded us it's still being worked on and their experimental code continues to allow Firefox to run natively on Wayland's Weston compositor.
Chromium is also Wayland-capable thanks to work done by Intel's Open-Source Technology Center. There's also been other basic GTK3/Qt5 web-browsers that will run natively on Wayland too if avoiding any X11-specific calls.