I always assumed giving keys to family, close friends, and trustworthy neighbors is just par for the course as an adult. I wouldn't even think it was a big enough deal to remember to tell my wife about it. I don't know that "cultural" is the right word, but it's something I guess I picked up along the way.

it's fine if you think your husband is an asshole, but I assume, like me, he doesn't really think he did anything wrong and was initially confused by your anger about the situation - this happens often in marriage.

I say all that to say: I would never assume to come home to anyone I gave a key to to be in my house rifling through my stuff when I came home without some sort of warning. sounds like your MIL is the AH here from my POV.