I think the "inflood" of foreigners should be taken into perspective. There was a time only recently, that there was a huge flood of "foreigners". The same arguments were posed - increased competition, taking jobs away, taking away lower paid jobs, disruption of social life. That was when women joined the workforce (other than the traditional roles of teacher, secretary or nurse). The pie simply grew bigger and overall, by large, most countries benefited from it.
It is probably easier mentally to accept women (us) as opposed to foreigners (them), but the economic reasons do not change.
What is more important is how to mitigate the speed and impact of these changes.
The crux lies with the measures not with the policy.