Especially if it is on a hot topic like religion or anything race related, it's likely that instead of learning anything you are gonna feel anxious and awkward. It's possible your parents are very progressive and have very similar views to you, but why risk it? Also it's possible the doc is about sex trafficking or something sex related and that is doubly bad- maybe your Dad is a pro-sex trafficking sex fiend, then what??
Something like The Room is not a good choice because the hilarious irony of the movie being "so bad it is good" is not going to be something you parents share with you. More likely you will have to repeat the phrase, "No, it's good because it's so bad!" over and over until you start to question if that's even true. Then you'll realize you are wasting time on watching a bad movie because it's "ironically good" which could open you up to a whole new world of judging your decisions.
Comedies are hard because everyone's sense of humor is different, and comedy between generations is often very different. If you sit down to watch a comedy you really like, there is a good chance one your parents will not get it at all and then the movie will be funny to no one. Having to explain why Jay saying, "Noochie noochie Brodie-man," in Mallrats is funny is very not fun and futile to begin with. But seriously, if you haven't seen it check out Mallrats, it's good.
Having to grab on to your parents because you are so scared would actually probably be comforting and reassuring, but it would also be weird and make you feel like you haven't grown at all and what are you really doing with your life anyway? And what if they are more scared than you? Then it may feel like a look into the future when you parents are older and you have to take care of them and deal with their fears. Either way it is time travel and not good.
Maybe see what's on TV.