I don't have any advice but am interested in seeing other people's responses as I will be renovating my laundry in the next year.

What is the size of the space? Can you close the door leading to the kitchen? If so, I don’t see a real need to add the separation. As you mentioned, it could make things look tight. Our laundry room is 12’x12’ and off the kitchen. It has 3 doors…to the kitchen, half bath and garage. In our case there’s a window above the washer, dryer and sink. I don’t think it would occur to me to close off the washer/dryer area, even with no window and/or smaller space. Being able to close the kitchen door is enough.

Hi our laundry room is half the size of yours 😅 it’s only 12x6. And yes there is a door that leads to the kitchen, and it swings into the laundry room. When the door is fully open, it ends right next to the sink. So if I install the shutters, when the shutters are open like in the picture, it would be in the way of the kitchen door when the door is fully open (hope I’m making sense). That’s why I’m hesitating…..
but it also doesn’t look too good when we walk into the Mudroom and see underwear hanging over the sink sometime 😂

We have a washer and dryer nook similar to yours, but ours is in the powder room. When we bought the house, there were bifold closet doors hiding the washer/dryer, which looked great. However, the doors were solid, not louvered, which was against code for our gas dryer, so we removed the doors. We could have put in louvered doors, but a subsequent remodeling project added ductwork so that the bifold doors no longer would have clearance to open enough. 

Long story short, I am considering using metal miniblinds or some sort of shade or curtains made of fire-resistant fabric instead. Something like this:

Since it’s between the garage and kitchen, guests will never see it. Make it functional first - do you fold and iron there? Do you have kids (or a husband) who will be dumping gear and kicking off shoes and dropping jackets everywhere? How many loads of laundry do you do a week? If you think the mud room portion will always be tidy and clean, and you don’t do much laundry, maybe hide the laundry nook. I’ve found that doors just get in the way and make it a bit more difficult to maneuver.

^Good point from SWF regarding doors getting in the way. We have a pocket door between our kitchen and laundry room that was installed by the previous owners of our house. It does make it more convenient.

We have a rather odd traffic pattern with our laundry room that requires walking through it to get to our guest bath. I have dreamed of a serious remodel moving pantry wall and door but a tension rod and curtain made of a bedsheet hides the machines when we have guests.

For Ratherbeatthebeach, there is a spray fire retardant you can spray on any fabric. The fire marshall made us spray all those bulletin boards at school.

So something like a shower curtain might work .