The most obvious: stay away from movies like The 40 Year Old Virgin, American Pie, 50 Shades, anything that has a lot of sex or where sex is the focus of the film. I do not wanna see Jason Biggs fuck a pie or hear Steve Carell describe what his virginal mind thinks a boob feels like while I try and scoot farther away from my parents' bodies.
Chances are you have already seen this movie a number of times, and every time you get a little more exclusive commentary on how much your parents like it. It's cool at first; you get to learn about your parents and their favorite movie, but after a while it's like, "Yeah, ok, I get it, you guys like Robert Redford. Yeah, I also saw him in All The President's Men. He was good there too."
There is a good chance your parents will not feel the same about the film, in which case you may be constantly defending it. If there is a joke or character your parents don't like in it, they will probably vocalize their feelings and then you find yourself defending why the "stink palm" in Mallrats is actually a good joke and a sign of the friendship between the two characters, and crucial to the audience understanding the characters. Mallrats rules.
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.