The terms (molding and moulding) have come to be used interchangeably. I prefer to say, ” I have moulding planes and some of them are molding because of the damp basement.” Actually none of my planes are molding. It might be an English vs. an American woodworking term issue such as rebate vs. rabbet or plough vs. a plow planes.
What you are referring to is actually a joinery plane not a moulding plane. There should be a little wiggle room in the fitting of the blade (sometimes referred to as an “iron”) to allow for alignment of the side of the blade with the side of the plane. You actually want the edge of the blade projecting a very tiny amount on the “wood side” of the cut. On non-skewed rabbet planes the edge normally should be square with the blade body. Check to see that the plane sole is flat and square and that the blade bed is square to the sole and sides. If everything matches up and wedge fits well then the issue has to be the alignment . Make sure the blade is not bent in a way to prevent good contact with the bed and wedge. It isn’t unusual to see blades ground out of square on old planes and the resulting difficulties in use often led the previous owners to lay the planes up and not use them. Because of this they didn’t become worn out and we still have them to enjoy. We still have to correct the issues if we expect to use them and that requires changes to the plane. I have seen planes with bed issues and the simplest fix was to purposefully grind the blade to match. It might be that the blade you have was not original to the plane.
You might hunt for a local woodworker that has experience with traditional tools to help you diagnose and correct the issue. Bill Andersons videos could probably help you out too.