Laundry closet door wont close
Trim molding will not hold a standard hinged door. It would take a skilled carpenter to move a hinged door outward. 

What part of the machines is preventing them being pushed further back? Could it be simply the dryer vent hose is interfering? Compare the specifications on the machines to the dimensions of your space. Is the washer hitting your back baseboard?

If it is just one projecting area on one machine, consider making a recess in the back wall, if a stud is not in the way (maybe not a good idea if this back wall separates your unit from the adjacent unit).

If you cannot shift the machines further back, either the machines are too large for a standard space for compact w/d or your space is non-standard.

If the former, return the machines as unsuitable for a standard space.

If the latter, remove the hinge pins and remove and properly store the door, but leave the hinges in place so the door could be rehung later. Hang a heavy curtain over the door opening, or install a hanging, sliding "barn door" over the opening.

EDIT My experience with doors is installing six pre-hung interior doors so I can imagine how I would proceed to move the door outward by 1 inch, but it would be a job and I couldn't say how it would look in the end. I suppose a skilled carpenter would make short work of moving the door out, but the end product might still look a little  strange.