My understanding of the graphics stack is not very deep so I might be a little inaccurate, hopefully someone will correct me when I am wrong.
X server provides the Xlib library that allows apps to draw to screen, listen to events, etc. To make app development simpler, higher level libraries like cairo or widget toolkits, which itself can use Xlib or higher level libraries, appeared.
Unfortunately, X comes from the times when applications could be trusted – programs were small and you compiled everything yourself, or later, a trusted distribution packager did it for you. Nowadays, we use a lot of software from external sources, even closed-source apps like Sublime, so the threat model has changed.
There are various methods of sandboxing apps but because X allows you to do basically anything, they are useless. Unless we wanted a full virtualisation like QubesOS does, a newer, more limited API had to be devised. Wayland offers that API.
If you do not rely on Xlib and use a higher level library that supports Wayland (like GTK 3) you are good. Otherwise you will have to upgrade. While there is a XWayland, a layer allowing to run X applications, it does not benefit from the better security and there is probably some overhead.
For a better, detailed overview of the stack see http://blog.mecheye.net/2012/06/the-linux-graphics-stack/
I recommend upgrading to GTK 3 since it supports both Wayland and X protocols. The Wayland support greatly outweighs the concerns about the look of file chooser dialogue. If you use some other APIs or even Xlib directly, more work will be needed.