Does Celebrating The Difference Destroy Equality?

Why do certain groups insist on parading their differences, whilst at the same time purporting to want to be accepted as part of everyday society?
I particularly have in mind group events like Gay (LGBT) Pride, Pride London etc.  While I do appreciate that this can be a strong reinforcement of shared identity (like biker rallies, anti-nuclear marches etc.) and that many LGBT persons experience great hostility and still feel excluded from, and discriminated within, society generally, do not such extravegently ostentatious displays of 'difference' contribute to the alienation rather then strengthening inclusion.

As we strive towards a society which does not discriminate against persons of different race, beliefs, sexual orientation, age, etc., I am baffled by the, as it seems, continual strident voices proclaiming loudly, 'we are different and we want everyone to know it'.

I would like to hear from readers because, although I had a gay Uncle, a lovely man now sadly passed on, and have gay friends, I do not have the perspective in this matter that a gay person will have.