I installed the debug package for the plugin and ran libweather.so through gdb. It reported a segfault, but the openSUSE page on gdb indicates it would save a file gdb.txt to the same directory it was run from, but that file did not save.
One of the Xfce devs wants a backtrace. This is what gdb displayed:
gdb /usr/lib64/xfce4/panel/plugins/libweather.so
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Reading symbols from /usr/lib64/xfce4/panel/plugins/libweather.so...
Reading symbols from /usr/lib/debug/usr/lib64/xfce4/panel/plugins/libweather.so.debug...
(gdb) run
Starting program: /usr/lib64/xfce4/panel/plugins/libweather.so
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Downloading 43.45 K separate debug info for system-supplied DSO at 0x7ffff7fbb000
Program received signal SIGSEGV, Segmentation fault.
0x00007ffff7fbd000 in ?? ()
(gdb)
Given the number of crashes I saw when I ran coredumpctl list, it appears when Xfce is loading in after login, that is when the plugin is crashing and restarting, likely from that illegal instruction, but because it crashes/restarts once at login, I do not see the image I posted above, that only appears on the second crash/restart.