There is no fundamental difference between Christian and Muslim extremism.
Think about how many people have been murdered in the Western world in random sprees of violence and the killer claimed purpose driven by the Christian Lord.
Not exactly a small number.
If you were a Muslim you would be saying that the assholes who take violent action in the name of their faith are loonies and not all Muslims are insane.
It is not the religion that is the problem, it is the people that choose to use it as a weapon.
A religious doctrine is just a set of beliefs, no negative connotations in any way.
All religious teachings (and some non religious) are doctrine.
I have seen the religious inequality in school before however.
It is not quite as you describe it, but it is present.
I went to public school, where no religion is taught but all are allowed.
A friend of mine has Scottish parents and wanted to wear some traditional garb for a remembrance day event and he was stopped from wearing the little knife (ankle mounted I think) that comes with the outfit. He argued that he would only be wearing it at an assembly with a few hundred people watching, and didn't plan on stabbing anyone with the three inch blade. They denied him anyway and he was pissed because it was the proper way his parents' people formally dressed. A few Indian kids were allowed to wear their full regalia, which included a small sword on their hip. Small meaning about a foot and a half long blade.
There is a much more lenient system in place for non-local belief systems than there is for the more common/widely accepted ones.
As for your links, I have personally experienced the Christian and Catholic versions of individuals overstepping the rules and regulations of religious teachings in public schools. Those articles are super shady, but they don't exactly put forth an image of Islam taking over our schools.