This question assumes quite a bit. Mainly, is forces the answerer to choose some sort of love as the cause of the tragedy, and I don't think most would agree love is at fault.
Considering family love as the culprit, one could only argue love is to blame if love is considered a cause of inflated ego, jealousy, hatred, misplaced loyalty and mob mentality. All of these ugly things are present within the feud between the Capulets and Montagues, but to blame love for them is a bit of a stretch. Spreading hatred in the name of love is equivalent to committing terrible acts of violence in the name of a kind and forgiving God; it doesn't make sense.
Romantic love could be to blame if one believes that love causes those involved to get a bit drunk on the good feelings of love and lose track of their inhibitions, emotions, and common sense. There have been studies showing these changes in the brain do occur, and there is certainly an argument that young Romeo and Juliet fail to display any emotional maturity or common sense in their decision making (aided by two adults who also fail miserably in common sense, Nurse and Friar Laurence).
However, Romeo is an emotional infant from the beginning, moping around like Eeyore without his tail from Act I on, and Juliet shows the ability to throw extended temper tantrum, but at least her loss of control is after her hormones get a hold of her.
So, as Shakespeare would like, pick your poison. Both COULD be blamed, but blaming either romantic or familial love for the tragedy seems to give love in its true definition a bad rap.