In Australia for pony club, chaps and half chaps are not allowed at pc or competitions. The first picture is of what we call half chaps. They are synthetic.
Leather half chaps are called gaiters, and are what we have to wear for pc and competitions. They must zip up at the back and be full grain leather on the exposed side. I have ariat concord gaiters, they are full grain leather on the outside, and suede on the inside. They are allowed.
If we do not wear leather gaiters, we must not wear any at all, and just have jodphur boots with or without clips.
I was flipping through friends pictures on facebook, my eventing friends - and one in particular was wearing paddock boots and leather 1/2 chaps. In these particular pictures, she was compeating at Richland Park - a very large 3* rated course where Olympic Eventers ride at every year.
This place is big, very serious and up there in "class" and "protocol" and she was wearing as described to be permitted.
Yes, they are permitted. I've had friends ride XC BN in suade half chaps without it being an issue. You would think that some people just don't want to risk their nice boots being cut off I guess..... *shurgs* I wouldn't go XC without my feild boots, they're wayyyyyyy to comfy!