This article claims that when Sony Pictures attempted to reboot the Spider-Man franchise in 2011, Marvel gave them a list of rules about how both Spider-Man and Peter Parker should be depicted on screen. These rules are;
Spider-Man
- Male
- Does not torture
- Does not kill unless in defense of self or others
- Does not use foul language beyond PG-13
- Does not smoke tobacco
- Does not sell/distribute illegal drugs
- Does not abuse alcohol
- Does not have sex before the age of 16, does not have sex with anyone below the age of 16
- Not a homosexual (unless Marvel has portrayed that alter ego as a homosexual)
Peter Parker
- His full name is Peter Benjamin Parker
- He is Caucasion and heterosexual
- His parents become absent from his life during his childhood
- From the time his parents become absent he is raised by Aunt May and Uncle Ben in New York City
- He gains his powers while attending either middle school or college
- He gains his powers from being bitten by a spider
- He designs his first red and blue constume
- His black costume is a symbiote and is not designed by him
- He is raised in a middle class household in Queens, New York
- He attends or attended high school in Queens, New York, or he attends or attended college in Queens, New York
These list of rules show a number of things about what both Spider-Man and Peter Parker must look like, namely that Spider-Man does not have to be Peter Parker (but he does have to be male), and that Spider-Man can be any ethnicity (but Peter Parker must be white).
So in short - yes, Spider-Man does have certain rules about how he must be depicted in film, but these rules do not extended to the ethnicity of the character unless he is Peter Parker. According to these rules, Marvel Studios could have chosen to use Miles Morales as their version of Spider-Man if they had wanted to.