To what extent are the other characters, especially Mercutio, vaguely responsible for the death of Romeo and Juliet?
Neither Romeo nor Juliet have anyone solid they can confide in. The parents and friends in their lives try to reach out but are either too self absorbed or oblivious to see what is happening with the two lovers.
Mercutio teases Romeo mercilessly but he doesn't listen to him. Mercutio wants Romeo not to be with a woman because he wants his friend back. He seems jealous--he is crass and disrespectful in his comments about Romeo's infatuation with Rosalind, and Romeo must think he would react the same way to Romeo's new love. And,yes, Tybalt and Mercutio both spark the events (out of well meaning but misperceived senses of honour) that lead to disaster.
Romeo's parents clearly care about him but they have no real rapport with their son. They have to ask others about him because they don't know.
Juliet's parents see her as a doting daughter (which, up to this point, she has been). There is no room in their relationship for her to be contrary, which, of course, is what teenagers do in order to grow. Hence, she can't talk to either of them, particularly not her mother who, though her references to Paris suggest she is capable of love, has married for position instead. She could not be expected to have sympathy for a young upstart daughter who wants to throw out her future for the love of a boy.
The few people they do trust--the nurse and the friar --are well meaning fools who try to act in R and J's best interests but who harm them more than help them.