Not possible to close protected branch
It is not possible to closed a protected branch:
No push is allowed to delete protected branches on Mercurial project. If that was your intent, you will have to unprotect it first
This is a little bit annoying because you have to unprotect it so any one with mercurial publish right will be allowed to push during the time we unprotect the branch.
It is worse if using wildcard pattern to protect many branches at once like branch/*
.