Why did the Nurse and Friar enable Romeo and Juliet to be married?

The failure of the Montague and Capulet families to show much love for Romeo and Juliet, respectively, has created an emotional void that needs to be filled. And over the course of the play it's the Nurse and Friar Laurence who proceed to fill it. The love between Romeo and Juliet is clandestine; it must remain a secret at all costs. It's necessary, then, for the two star-cross'd lovers to have people on whom they can rely completely.
The Friar is presented as a good man, an endless source of wisdom and sound advice. He's deeply sympathetic to the young lovers' plight, but he wants to see them get married, because he thinks that it will somehow heal the seemingly irreparable breach between the Monatgues and the Capulets. If Romeo and Juliet get married, thinks Friar Laurence, then the long-running feud may very well end.
The Nurse is less consistent in her support of the marriage. She has a strong maternal instinct towards Juliet, yet at the same time is ultimately subservient to the prevailing social standards. Initially, she encourages Juliet in her desire to marry Romeo. Yet social convention soon prevails, and the Nurse changes her tune, advising Juliet to marry Paris instead, and forget all about Romeo:

I think it best you married with the County. O, he's a lovely gentleman. Romeo's a dishclout to him. (Act III Scene v)

Though the Nurse always genuinely believes herself to have Juliet's best interests at heart, she simply cannot share the young lady's elevated feelings of romantic love. The Nurse is a rather bawdy character, much more down-to-earth than the achingly naive Juliet. But more than anything else, she's still a servant, and that explains why she changes her advice. What matters to her more than anything else is Juliet's position in society, and not the dictates of her amorous young heart.