Slap them.

No! Of course not, that would be very counterintuitive.
Don’t physically assault anyone, that will just make matters worse.
The best course of action, by far, is to communicate with them openly and honestly, as well as listen to them. I know, damn. The hard way. Why isn’t the right way ever the easy way?
Give this a try?
Listen
Listen to one another, really examine why you both act the way you act. Check out my blog about examining emotions, it might help. Sit down with the person and tell them how you’re feeling, listen when they tell you how they are feeling too.
Start with one small habit.
See if they will make one small change in one small area of their space. This makes it feel less daunting for them to make a bunch of changes all at once.
Tricky tricky
Create a system that doesn’t allow them to be disorganized. If they always leave dishes in the sink, then take all the dishes away and put them in a vault to only be used when guests come. Leave 2 cups, 2 plates, 2 bowls so that you each get one set. This way, they constantly have to keep their dish clean if they want a plate or cup to use. Now they are forced to stay organized because it’s really the only option. Or, at the very least, dishes can never pile up!
Now, when implementing a system like this make sure that they are okay with trying it, don’t surprise them with it, that might lead to yet another serious disagreement.
Separate space
If it really comes to it, where they won’t change, and you can’t handle their clutter anymore, then you could try separate spaces in the house. Separate shelves in the refrigerator, separate sinks for dishes, and bathrooms for getting ready, as well as separate closets for your clothes.
It may not be ideal, but at least you get a space that you can have to your needs and specifications the way you want them.
Be patient
At the end of the day, you just have to learn to be patient with them and their transition to becoming more organized, or accept the fact that they may just never change.
So whatever you do, don’t slap them, if you can, embrace them, give them a warm, long, hug and reassure them that you’ll get through this together.