I believe what has changed is not the “cheese” but the labeling laws. That yellow cheddar-like product now labeled “cheese food” or some such should do just fine for your recipes (and may be the same thing that once would have been called “cheese”). So will a very mild cheddar (see below) unless you need something that will melt smoothly in which case Velveeta may be just what you are looking for. Many 50s recipes used it and it was invented for the purpose of making smooth cheese sauces (and I recall lots of adds for it on 50s TV and in 50s magazines).
Another thing that has changed since the 50s is the American awareness of and respect for food products from other countries. “Cheddar” is actually an English cheese. While we tend to call domestic copies of it “cheddar” nowadays, they probably didn’t bother in the 50s since back then most Americans considered American products superior and were happy to buy “American cheese” which was, in reality, a cheddar-style cheese.