I have to disagree. European Union should be Union of Nations not a one country without a face. If we take Nations out of equation we will lose our identity.
I will say it again. The word you looking for is xenophobia.
How would you lose your identity? Unless you base your entire identity on your nationality.
It's big part of our identity. As being born in European country I share most of the values of Christianity. That is despite being an atheist. If we try to diminish that values we expose ourselves to indoctrination of values of others maybe not as liberal as our cultures. We shouldn't, in my opinion, dilute our identity we should cherish and embrace it.
I give you an example. In Europe, at the moment, there is a trend to invite and harbour people from Middle East. As much as noble it is, a big part of these people have no intention to integrate and at least respect our values. It is quite opposite, the core of their values is to indoctrinate others to their liking.