For an American anecdote, my father taught at a small rural public university, and he encountered students who were functionally illiterate every year. They were almost always from small rural schools. In a larger school, a kid who couldn't read would have had difficulty passing classes, received remedial instruction, been assessed for intellectual disabilities, and so on. Unless they had extremely serious behavioral problems or congenital intellectual disabilities, or they dropped out of the system entirely, they would learn to read! In a school system that is smaller, less impersonal, without extra programs and resources for a teacher to fall back on, it's really hard to label a kid a failure and deny him a diploma just because he's falling behind academically and the unsupported, often barely trained teacher can't get him up to speed. Especially in a small community with lots of illiterate people working and earning a living, it's hard to justify stigmatizing a kid that way and denying him an essential part of a normal American life, namely to go through school with his peers and have all the normal school experiences. So kids get passed along from grade to grade and then (why should 12th grade be different?) they get a diploma.
There was also, I think, a kind of naive view that intelligence was a pretty broad spectrum and a lot of kids were naturally going to end up illiterate. This was understandable if your point of view was restricted entirely to a small rural area where a small but significant number of adults were illiterate. It just seemed natural for some people not to take to reading, and that was just a normal part of life, not something a person should be punished for. (Most teachers had a much more progressive and modern understanding, and I really don't want to overstate the prevalence of this view, but a handful of teachers here and there is enough to produce a steady trickle of children falling through the cracks.)
Another factor was that there was not a uniform understanding of the purpose of high school and college credentials. Most people accepted the notion that a diploma should guarantee a minimal set of skills — functional literacy included. They valued the education and skills that their children were getting. Occasionally another feeling showed through, though, which was that educational credentials were a way of granting life success to some people and denying it to others, and requiring kids to succeed academically in school was just a way to perpetuate class and racial distinctions. This sentiment came to the fore when my state adopted a minimum skills test that kids needed to pass in order to get a diploma. This test was labeled "evil" by some people in my community because it pointlessly (in their eyes) denied their kids a chance for a normal life. They felt no anger or anxiety about the fact that their kids struggled with reading to the point where they couldn't pass a state basic skills test. They were only angry about their kids being denied an important life credential. And with Jared Kushner getting a Harvard diploma, you can't say it was entirely a made-up concern, even if they did adopt a counterproductive attitude towards their kids' education because of it.