I mean, it's ridiculous that missing lectures is a big deal and the school is wrong in that instance. But you have some misconceptions about call. It isn't true that you always have the option of trying to switch dates. First off, some residencies don't allow you to switch. When you're scheduled, you're scheduled. Second, sometimes rotations are arranged in such a way (a year in advance) that allows you to be on call certain times of the year and not other. Like if you're on neuro, it would be ridiculous to expect you to take medicine call. So that month, you can't take medicine call so you can't trade with anyone that would necessitate you working their call when you're on neuro. Likewise, if someone others are on elective, they're either not going to be able to or want to switch call with you. Don't ever think you have 20-something people to juggle call with. Most likely, unless you're at a gigantic residency program, you will have only a few who are actually available and then it's up in the air if those few will do it. And all that is if your program allows switches.
It is true in some situations you will be able to switch, but you're realistically not going to get through training by switching/missing all devout holidays. It just won't happen. I'm in psych and even in psych, perhaps the most laid back and chill of all residencies, we all worked at least a handful of devout holidays. Now if you're only considering, say, Easter as a devout holiday, then you can possibly get through training never working Easter Sunday. But if, from a Christian standpoint, you want every Easter, every Christmas/Christmas Eve, every Good Friday, and every Ash Wednesday off every year, it's just not realistic that's going to happen, even in psych, and if you're "that guy" trying to trade every single holiday, you're quickly going to be disliked by your colleagues who are no more excited about working them than you. You will work devout holidays and going in with that expectation will save you a lot of disappointment.