Morally, they should probably do what's best for their constituents, particularly their most vulnerable constituents, rather than necessarily what their constituents think they want.
If that means bringing the ire of those wielding the voting power, then so be it.
See, you assume 'morally' means stay in the EU? I don't see it that way, our relationship from a 20,000 mile view is not that great, in fact the absolute best reason I've heard for staying in the EU is to fight it from the inside and try to influence it from the inside..
The fact is, we are a more outwardly looking global thinking nation, we alway us have been (e.g. Common Wealth) and that's part of what makes us as great a country as anyone other great country..
Europe is very inwardly looking and self serving, they have deliberately set up CAP/tarriffs etc to protect the main French/German industries, giving them maximum protection from a world market.. this is not what the UK has ever wanted, we fought to not impose tarriffs on Steel, despite it hurting the steel industry because we look outwardly..
We kept the £ and want our own currency because we have no faith in the Eurozone...
Sum all that up, and clearly we are at odds with Europe, I just believe that there is far too much evidence (historically) that the EU are really in it to protect French / German interests and our outsider behaviour we've exhibited (not taking the Euro, fighting for global trade) sealed our fate.. we got to the point brussels had enough and said 'No more'.. that essentially means we either assimilate into Europe or stagnate..
I also think that we need time to assess a game plan.. see if we can make it work, then pull article 50.. be in order to do that, we can't sit here looking all doom / gloom, we need to accept what kind of country we are, and make huge efforts to assess if we can make it work.. If after a good few months of trying to get a good plan we come to the conclusion that it really can't be done, then I'll happily change my mind and vote remain on another referendum, although I'd like to say if we embrace the EU, embrace it, get in the Euro, start looking inwardly, and get our industries protected (If its not too late).