Can someone with Sun's putative Render extension figure out what to check and
make sure it works?

That's what I did.  Here's code that seems to work:

        {
          /*
           * Sun advertises RENDER, but fails to support 32-bit pixmaps.
           * That is just no good.  Therefore, we check all screens
           * for proper support.
           */

          int screen;
          for (screen = 0; screen < ScreenCount (xdisplay); screen++)
            {
              int count;
              int *depths = XListDepths (xdisplay, screen, &count);
              gboolean has_8 = FALSE, has_32 = FALSE;

              if (depths)
                {
                  int i;

                  for (i = 0; i < count; i++)
                    {
                      if (depths[i] == 8)
                        has_8 = TRUE;
                      else if (depths[i] == 32)
                        has_32 = TRUE;
                    }
                  XFree (depths);
                }

              if (!(has_8 && has_32))
                {
                  g_warning ("The X server advertises that RENDER support is
present,\n"
                             "but fails to supply the necessary pixmap support.
 In\n"
                             "other words, it is buggy.");
                  x11display->have_render = GDK_NO;
                  break;
                }
            }
        }

Can you test with the attached patch?

Created attachment 44 [details] [review]
Check depth support before reporting Render support

I think the patch will work; synthetic testing appears to succeed.

Docs could be made to refer to Sun patch:

Patch-ID# 113098-04
Keywords: X11 Xrender
4770510 RENDER should not be advertised unless required depths are supported

Since the patch appears to have survived the past 7 years in libXrender, the reporter hasn't needed to follow up, and nobody's complained, I'm closing this as FIXED.