Integration means becoming part of a group, a community, but it would be wrong if that means giving up who you really are. Rather, genuine integration is a two-sided process that brings people together. That way, the immigrants can enrich the local culture. ‘Economic migrants’ may be in less urgent need of help than war refugees, for example, but they will mostly have undertaken the harsh journey to your country for a serious reason.
Can you refuse to help an entire group of people if one or two among them are abusing your goodness? In answer to a perceived or real ‘religious invasion’ we can invite our societies to (re)discover the Christian faith. We are free to live our faith and proclaim it (Mk 16:15), but have to accept that others too have that freedom. Every act of violence must be acted against in accordance with local law.