1) Visit facebook.com
2) Type control-X.  Note that "C-x" appears in the minibuffer/echo area.
3) Type a sequence of j's and k's.  The screen scrolls down to the next item when j is pressed, and it
scrolls up to the previous item when k is pressed.  The "C-x" remains in the echo area, waiting for the
next key in the sequence that began with control-X.

Another site I visit frequently, inoreader.com, exhibits a similar problem.

In particular, this behavior means that I cannot invoke the kill-buffer command using its default
keybinding (C-x k) when viewing either of these sites.

Not all sites manifest this issue.  When visiting mail.google.com, I can invoke kill-buffer using C-x k,
even though that page also assigns a function to the k key (it moves the marker to the previous message).

The issue occurs even if I totally remove my ~/.conkerorrc.

My noticing the issue seemed to coincide with my recent update of xulrunner from version 19.0b6 to
version 27.0.1.

If it helps at all, I did a binary search just now and found that Xulrunner release 25.0 is the first one
that displays the bug I described.  The previous version, 24.0b10, is fine.

This is a long-standing issue that gets down to how Conkeror's input system works.  There
are various methods of working around it, such as key-kill-mode.  The problem is
aggravated on some sites depending what user-agent string you send them, so you can
experiment with that, too.  This has been an increasing problem because more and more
websites use the keyboard.  Ultimately the input and focus system will have to be
redesigned; some work has been done in this direction in the 'point' branch.