Wayland developers for months have been working on primary selection support to mirror what is offered by X11. That work will soon land in the wayland-protocols repository, but now hitting crunch time for the GNOME 3.20 release next month, an early implementation has landed for Mutter.
The work done by GNOME developer Carlos Garnacho is outlined via this GNOME BugZilla entry: Implement primary selection protocol. "This adds the ability to middle-click paste between/across gtk+-wayland and x11 apps."
That work was committed yesterday to the Mutter repository as one more step towards a better GNOME 3.20 Wayland experience. The commit explains, "This protocol is an internal mirror of the primary selection drafts being proposed for wayland-protocols."