I'd be mad about it. I'd be mad about it whether it was someone with whom I clashed about other things or not-- to me, it's just a decision that parents make for their little kids and that later kids will make for themselves. Hair is not for an outside party to decide. Yes, it'll grow back, but you and your kid are the ones who have to go through it looking dorky until it does.
I would be less mad if she had taken him to have it professionally done by someone who knows how to cut bangs straight... but still annoyed. I still think it's overstepping.
Also, I would make sure that someone (and it could be your husband if you're not up to doing it yourself) tells her that you don't want her to ever do it again/that it wasn't actually helpful. It seems like a common sense thing that anyone should know... don't cut someone else's kid's hair without asking... but you know she has her own very different world view and it's obviously not common sense to her, so someone needs to tell her directly.
Edit to add: also? Really? He sent the post to your FIL? Headdesk. Headdesk.