A green-band trailer is always the color green and indicates that the preview is suitable for all ages. Motion Picture Association/Wikipedia
On the simplest level, studios and theater owners try to pair trailers with the audience who’d presumably go see their associated film. They often use something known as a “quadrant system” that divides cinema audiences into four groups: women under 25, men under 25, women over 25 and men over 25. (This system may have internally evolved to also represent other forms of gender identity.) Trailers are matched with the quadrants they presume are in the theater watching them.
For instance, an animated film with a G-rating is going to have plenty of viewers under 25, but most will be there with their parents, who might be interested in some adult content. Of course, none of that adult content should be inappropriate for young viewers, so this will preclude certain trailers intended for the “over 25” crowd. Ultimately, theater owners don’t know as much about the people in their seats as streaming services might know about the person on the couch. That’s one reason why they divide their audiences into such broad quadrants.
Just as movies have audience ratings from the Motion Picture Association of America (MPAA), so too do trailers. You can tell the rating of a trailer by the color of the screen that comes at the beginning. A “green-band” trailer is deemed appropriate for all audiences; you’ll see these before all types of films. A “red-band” trailer is intended for “mature audiences only,” and these may feature the same kind of edgy content you’d see in an R-rated movie.
It’s up to theater owners to decide what types of trailers their audiences see. (Generally you would see a red-band trailer only if you were going to an R-rated movie.) If they have a policy against red-band trailers, studios will typically furnish them with green-band alternatives. This doesn’t mean that audiences have to be shut out from seeing these red-band trailers if they really want to. Thanks to YouTube and numerous video streaming sites, they’re only an internet connection away.