Just to take a little bit different take on the question, the reconciliation BETTER be genuine because Shakespeare's Romeo and Juliet is a tragedy, and as such does end with death, . . . but should also end with an inkling of hope. (This, of course, is the opposite of a comedy which would end in a "happy" marriage, . . . but should also end with something at least a tad disturbing.) To suggest something different is to destroy my entire thought process regarding comedies and tragedies. SO, although I'll admit that most of the words of professed reconciliation come from the Prince and not the heads of the feuding families themselves (which in itself is a bit disturbing), the heads of the Montague and Capulet families do participate in a few of their final statements of the play. For example, Lord Montague and Lord Capulet do shake hands as evidenced by Lord Capulet saying, "O brother Montague, give me thy hand" (5.3.309). I believe a handshake in itself does constitute a significant bond. In addition, I think honoring the child of the opposing family is a grand statement of reconciliation:
Lord Montague: But I can give thee more; / For I will raise her a statue in pure gold, / That whiles Verona by that name is know, / There shall no figure at such rate be set / As that of true and faithful Juliet.
Lord Capulet: As rich shall Romeo's by his lady's lie--/Poor sacrifices of our enmity. (5.3.312-318)
Done, and done. But what's truly exciting is that this is one of those glorious examples when the text can be used to support either theory. It's so wonderful when that happens, . . . as it shocks the heck out of my advanced students!
I think the end to feuding and family fighting in the play Romeo and Juliet by William Shakespeare needs more than just the reconciliation of the two family dynasties - the Capulets and the Montagues. The Prince's speech concedes that he too must learn from mistakes, ommissions and errors of judgement. He 'winke'd' at their misdemeanours for too long.Although the two families have been humbled into a clearer realisation of where their hate has brought them to, the deaths of the children/young people was partly facilitated by his tolerance and failure to act decisively. The grief of the families is genuine and painful and does seem to shock them into a need for genuine behavior change. However, for this new adherence to city laws to continu down the generations it will need the zero tolerance of anti-social behavior to be far more rigidly enforced by those the Prince represents.
True, the ending does has the reconciliation of a comedy. I think the deaths of each family's only child only spells a continuation of the feud. Knowing this, I think Shakespeare does add Lady Montague's suicide to the death toll to make a reconciliation more plausible. Add to this the Prince's continued strong stance against the fighting, and a reconciliation is politically savvy for both families. I think Lord Capulet's statement of dedicating a gold statue to Lady Montague is a bit much.
In other "honor cultures" in which familial revenge is common, no such levels of reconciliation have been achieved, and certainly not as conveniently. But, Romeo and Juliet was written by a young Shakespeare, still a bit green and idealistic. He more engaging and mature tragedies were still to come.
I suppose your answer to this lies in how cynical you are about the world. You can find evidence to suggest either that it is genuine or that it is not.
You might argue that it is genuine because it has been brought about by such a horrific event. If the two men really loved their respective offspring, they might well be so taken aback by the deaths of those children that they will sincerely repent of what they have done.
On the other hand, they might just be saying these things in the heat of the moment. You can see a suggestion of this in what they say about the statues they intend to raise. You can say that they have already started to compete, with Capulet saying that his statue of Romeo will be just as good as the one that Montague raises for Juliet.