What is the importance of Romeo and Juliet's isolation from their families?

The fact that Romeo and Juliet are isolated from their families makes it easier for them to disobey their parents and for them to hide their secrets from them.

Both Romeo and Juliet are isolated from their families.  In the beginning of the play, Montague complains about how Romeo spends all of his time brooding, and not talking to anyone.  He says that his son usually shuts himself up or wanders around alone.

MONTAGUE

…But he, his own affections' counsellor,
Is to himself--I will not say how true--
But to himself so secret and so close,
So far from sounding and discovery,
As is the bud bit with an envious worm,
Ere he can spread his sweet leaves to the air,
Or dedicate his beauty to the sun. (Act 1, Scene 1)

Although Romeo does have friends, he is disconnected from his parents.  His father says he is happy that Romeo was not at the swordfight in the marketplace, but it cuts both ways.  It’s good that Romeo is not a fighter, but he also has no family pride.  Unlike the servants, he is not passionate about his family’s cause. 

Capulet has a similar problem.  Juliet is young and flighty.  She is the only daughter he has.  When she sees Romeo and finds out he is a Montague she has a momentary hesitation, but it is just that.  Her family loyalty does not last long.  She is closer to her nurse than her mother, and asks her nurse to help her arrange the marriage. 

It is because Capulet has so little contact with his own daughter and is so unaware of what is going on with her life that he doesn’t even realize that she has already gotten married when he tries to marry her off.  He doesn’t ask her what she wants, and he only gives her a few days.  When she objects, he threatens to disown her or beat her. 

CAPULET

Hang thee, young baggage! disobedient wretch!
I tell thee what: get thee to church o' Thursday,
Or never after look me in the face:
Speak not, reply not, do not answer me;
My fingers itch. (Act 3, Scene 5) 

Like Montague, Capulet has no idea what is going on in his child’s head.  His heavy-handed approach backfires and he sends her running to Friar Laurence to fake her death.  The cluelessness of the Montague and Capulet families of what was really going on in their children's lives was definitely a contributing factor in their children’s deaths.