I watched Fruits Basket when I was in middle school but watching privately in your house is different than a school backing it as family friendly. That means you basically have to turn down large parts of shows - large parts of Dragon Ball Z can't be shown because of constant violence and blood, large parts of Sailor Moon can't be shown because of perceived nudity every episode (when they transform), and large parts of Pokemon can't be shown because of animal abuse. The list sadly goes on and on and exists.
I work at a school where we can show PG13 things but not anything above. I was surprised "Tokyo Godfathers" is rated PG13 -but it is. "Catnapped" is an amazingly inovative adventure from the mid-90's and it would be perfect to show in a school setting until one scene very late in the movie that implies heavily animal abuse as a plot point. I can show it where I work, but you wouldn't be able to show it to 12 year olds.
However, if you can, look to see about getting waivers done. Send the kiddos home with the paperwork that says "dear parental units, I would like to show this movie (name the movie or series) in my classroom. it contains this material and you're welcome to look it up. I would like to share it with the students to (further their multi-cultural educational experience blah blah something that helps "education" would be a great sell for parents)." and then ask them to sign the waiver.
That way, parents who are 100% against anime because of their faith can have full control of denying their children access to this at the school. And yes, that will be a conversation that will happen. One of my friend's in school, her parents had strong faith beliefs that meant Pokemon was borderline okay, but Fullmetal Alchemist was 110% not, and Inuyasha was so far off the "okay" list....