I would have to concur with the previous response that, at age 17, I don't think Hinton would have been particularly interested in politics.
Though I would further speculate that although there was a tremendous amount of turmoil in the 1960's: Vietnam War, Civil Rights movement, Ceasar Chavez and the Migrant Workers movement, three assisinations, etc, none of these issues has anything to do with the Curtis Brothers or any of the other characters. Hinton was focused only on the issues of the Socs and Greasers. And these issues had nothing to do with race or politics. Since I believe she was writing for a young adult audience, I think discussing politics would only have detracted from the story and lost her intended audience.
I would speculate that there are two reasons why she might have done this:
First, when S. E. Hinton wrote this book, she was very young. In fact, the book was published when she was only 17 years old. It seems likely to me that she was not particularly interested in political events at that stage in her life. I know many teens are not.
Second, she might not have wanted to "date" her book. She might have wanted to make the book seem more like it would fit in any time and place. After all, the themes that she explores about teens and their place in society seem to fit with pretty much any time period (one reason why the book is still read now). If she had put in political stuff, people nowadays might feel less as if the book applies to them.