If a migrant adapts to the culture of the host country (i.e. respecting the beliefs of the indigenous people, celebrating the holidays of the country, learning the language and speaking in the accent of the country), then they should be welcomed with open arms. However, if they try to impose their beliefs on the people in the country then they shouldn't be allowed in the country.
The UK, the greatest country in the world, has immigrants from the West Indies, Nigeria, and the Indian Subcontinent. The vast majority of them are diligent and friendly people. They speak in the Cockney accent, celebrate British holidays, and many of them marry native Brits. However, migrants who want to impose Sharia law on the UK should be turned back, regardless of what the EU says.