I know some cultures find things acceptable that might be considered rude elsewhere, including here. There are some questions that, if asked, I might deflect or point blank refuse to answer, and I wouldn't appreciate anybody going through my personal belongings. Years ago I was in hospital for a while and my sister had a friend who, along with her couple of weeks old baby, had been made homeless - I let them stay at my flat. When I eventually got discharged and had the opportunity to talk to her she said something along the lines of....I know you haven't lived here yet and I did look in kitchen cupboards for cooking utensils, pans, crockery etc but anything else with a cupboard or door I figured would be private. I felt good to know I'd helped a decent person at a difficult time and that she had been respectful and not nosey (even my mail was in a neat pile). Come to think of it my sister has had about half a dozen good friends from school and 40 years later they still arrange an annual holiday together. There will always be family clashes, cultural clashes etc we just need to find ways to get on, compromise, talk about any problems before they become major issues.
If the ex was comfortable explaining the OCD maybe your daughter-in=law might be more considerate and understanding. If she has a difference of opinion about what food is eaten would it be an idea to see if she would like to cook sometimes, shop, choose ingredients or cooking methods etc. She might be a nosy person or she might be trying hard to fit in, adjust, be accepted and be part of a new family. Keep conversations light rather than confrontational - you might both learn about each other and there might be opportunities to slip in nuggets about things that might be construed as intrusive. Good luck - I hope you can all find ways to rub along.