This would then dismiss every CoC-related effort, because most enforcers do little regarding humans being persecuted in other countries...
Apply your comment to the monks then.
At the same time I do believe that the spirit of Christianity, Islam and most other religions is inherently good, positive and inclusive and there are definitely people that use that as a guide to improve themselves and their lives.
BUT, even if the spirit is good, the actual history says that these organisation shouldn't be held on a moral high ground for anything because they don't deserve it.
Moreover, even today, chances are that if you are a non-conforming individual in a very religious community you are subject to isolation, bullying and shaming.
And that's why I find it of very bad taste to use this as a CoC that should guide integration: if I have been bullied from my ultra-religious community, for example because I am bisexual, then I'll not find that a very welcoming sign.
To be fair the Benedictine order wasn't one of the worst orders with respct to whole witch/heresy craze but that kinda furthers the irony of the whole situation: watching to the other side while someone is being persecuted (or bullied) puts you closer to the oppressor than to the oppresed.