Honestly, it depends on the structural aspects of the house. In the 50s, we were well into stick framing where most houses used a center support wall. Some builders were still using balloon framing, but it was becoming uncommon. Ways to check this is in your basement or crawl space. If there are supports running down the center of the space, that is where your structural support wall is. If your cabinets are built into that wall, care must be taken to insure support remains adequate. ( architect ) If the cabinets are in a wall perpendicular to the structural wall, there is a much better chance they can be removed without consequence.
Unfortunately, Although I have never heard of cabinets being structural, the 50s were still a time when people could design and build their own houses with little interference from code enforcers and inspectors. So, it would be impossible for anyone to give a definite answer without looking at it.