To me it is not even about the picture, it is about the wife being annoyed at the way her husband behaves around his mother and defers to her interests. She wants him to assert himself, he just wants to take the line of least resistance and avoid any potential conflict.
The poor guy is on a hiding to nowhere no matter what he does. Personally I would just take the picture down. It would be more hassle than it is worth. If such a small issue creates this much conflict I think they have much bigger things to worry about.
No, she wants him to stand up for himself and her, I don't think that's a small issue.
He is also worried that knowing he likes this sort of thing will change his mother's view of him. Liking what appears to be a tasteful nude is hardly earth shattering and if that would significantly change his relationship with his mother then his mother is the problem not his wife.
I don't think it's so always so easy when dealing with family. Yes, the mother is the problem. Her disapproval/judgements of adults is wrong. It would be wonderful if the husband here didn't give a flip what his mom thinks and would be totally ok if she never visits him again...but it's just not that easy. I might be willing to take a tough stance when it comes to a friend, or a cousin, but right or wrong, I tend to give a lot more leeway to my mom.
If all this is about is moving one picture, then I do think, were I the wife, I'd just move it. It would be totally different if it were about moving several things, or pretending to have a different lifestyle, etc. But one picture (which I'm going to assume it is taking the letter at face value), not that big of a deal.
And if we are going to conjecture that this is more than just the picture, then we should also leave open the possibility that mom, regardless of who purchased the picture, would take it all out on the wife. She turned her poor son to sin...And now things are more strained for her. While the wife may be totally ok with it, it would still be nice to recognize that the husband is thinking of her too.
At face value, I get it. No one should have to hide their stuff from a guest. She shouldn't have to move her artwork simply because her MIL won't like it. And her husband, an adult, should have the guts to let mom think what she's going to think and 100% support his wife. That's definitely ideal.
I just think these aren't that simple. Real relationships
and emotions do play into it. And if it were me, I would consider if not moving the picture out of principle was worth all the drama and strained relationships
that would result? For a friend...maybe. But, I'm not so sure about my mom.