There's no such thing as fate or blame in tragedy, at least not by the characters therein.
Shakespeare is to be blamed for the tragedy, not anyone else. He controls fate only. He knew he as writing a tragedy, that all would die, and so he planned it that way. Tragedy is not realistic; it is engineered by an author for disaster. No single character, therefore, can be blamed, not even Romeo and Juliet or--in his more focused ones--Othello, Macbeth, Hamlet, Julius Caesar, or King Lear.
Tragedy is only tragedy in hindsight. No one recognizes it at the time. If any number of events might have gone the other way (Mercutio's death, Tybalt's death, Friar John's letter), then the tragedy would have been avoided. But then, that would have been either a very boring or an absurd play. Audiences are attracted to wildness, to when things go horribly wrong (tragedy/myth) or right (comedy/romance).
Shakespeare wrote a comic version to Romeo and Juliet called Much Ado About Nothing in which tragedy was avoided by better communication. The staged death of the bride was known by several, instead of one. The bad guy was caught, and all was blamed on him. Not one, but two couples married. That's more realistic. But, no on asks those questions: "Who is blamed for Hero's marriage?"