I am a psychologist, that's the type of social scientist I am.
Now that that's out of the way, coming to your question, you think that being Muslim means one thing? Right? We should implement the Sharaih? Right? Ok, what is the Sharia? Do you know that there are various interpretations of it? One does not agree with the other. So who's should we implement? I will let you know of an example, the place from where I did my A Levels has law programmes and we had a seminar on Islamic sources of law and boy, oh, boy, was that an eye opener: it broiled down to a brawl over the authenticity of a number of Ahdees which were considered legal by a number of Salafi scholars but not by a few others and none at all by the Shia sect. I was surprised to see people get so heated and not relenting and that's the point: faith is about belief, you really cannot argue over it. If you do, it gets ugly.
However, law by consent-authority, which is the base of modern civil systems can work, let's say that we would put laws into place which have 2/3rds support of the parliment and we'd implement it, that takes away that problem and as a nation we can use the Quran for our guidance.
Thirdly, true religion will always remain a part of the identity but that's it, it will remain a part. For example, other sources of identity still play an influence: Lahori, Punjabi, Pakhtuun, Sunni, Shia and so on. So it's not just the singular source of identity and that's why you have problem when you make it so. Look at Isreael, it was created for Jews, irrespective of their denominations, so were we, the denominations do not matter. The Jewish scriptures influence the State of Israel but so do secular philosophies, they don't have a problem, why do we? I'll tell you why: because we are convinced that our interpretation is the correct one and on that we are divided and fooled. They don't. So shouldn't we.