All X11 window managers are capable of managing GTK3 applications.
All X11 window managers are capable of managing GTK3 applications.
The downside to these changes is that several GTK3 features were horribly broken outside of GNOME's default window manager. I've seen at least five or six window managers that would freeze applications with the mouse grabbed as of GTK3.2: click on the wrong part of a menubar or on the resize corner and you had to resort to the keyboard to kill the offending application before it or your mouse would work. Version 3.4 or thereabouts has fixed these bugs for the most part; even window managers that don't support much in the way of ClientMessage-based window manager protocols should work fine now. But for some time GTK3 did interact very poorly with most window managers.
http://bugs.debian.org/cgi-bin/bugreport.cgi?bug=630972
That this was so hairy and bug-prone is, in my opinion, a symptom of interacting with the ugly beast that is X11. If you read the code of the affected window managers and GTK, you would probably agree.
What's your opinion on Wayland? Specifically, how likely is it that the reliability and consistency of the graphical parts of desktop Linux will improve if the applications I use the most are ported to Wayland?
Despite the pains, X allows window managers to arbitrate over window management policy relatively effectively. From what I see so far, it seems that this will be a less clear-cut scheme in Wayland, given its clientside window management and decoration setup. Individual applications will have more freedom to misbehave in terms of custom titlebars etc. and refusing to cooperate with management actions. In an environment where GTK, Qt, wrapped X programs, and other toolkits will be coexisting, there's a lot of room for implementations to behave differently in ways that will confuse and upset users. Whether this will actually be the case is yet to be seen, but I've never seen three different software projects implement a feature in exactly the same way without sharing code.
As the saying goes, we live in exciting times.
Users of desktop Linux live in exciting times, you means.