Critics of uncontrolled mass immigration claim that importing large numbers of Arabs means importing backward attitudes toward women into Europe, which will inevitably cause problems.
Of course they're right, as a recent ambitious Promundo/UN study of gender attitudes in the Arab world shows. Only about a quarter of the men polled have liberal attitudes comparable to those of the majority of European males. Large pluralities and sometimes majorities of people in the four countries studied (and not just the men) believe males should exercise guardianship over female relatives, that women deserve to be beaten once in a while, that women should stay at home, and other prejudices we're all familiar with.
So is the solution to ban all Muslim immigration? No, although doing so would not violate any law. Countries are permitted to engage in intentional racial or religious discrimination when they decide which foreigners to let into their countries, and they do it all the time. With a few exceptions, Japan keeps out non-Japanese, Israel lets in only Jews. Nobody has any right to live in a country other than the one they are a citizen of. Countries have every right to screen people whom they let in to ensure they're likely to adapt successfully, and the best-run places on earth do exactly that.
So a European country can ban all Muslim immigration, as majorities of French and Austrian people want. But I personally don't believe this is necessary or justified. What European countries can and should do is only allow in educated people. There is an extremely strong correlation between increasing levels of education and more tolerant social views. So it's no surprise that the study of Arab populations concludes (pdf, pp. 47-48):
These overall attitudes toward gender equality were assessed using the Gender Equitable Men (or GEM) Scale, an internationally recognized and validated composite measure of attitudes toward men’s and women’s roles and rights....
Younger, urban, wealthier, and single women also scored higher on the scale. Education is clearly driving support for equality. Both men and women with higher education, as well as those whose mothers have higher education, scored higher on the GEM scale, women notably so. Parental division of household labour ... also contributes to more equitable attitudes; men and women whose fathers participated in housework also held more gender-equitable attitudes.
If you want immigrants who will respect European values, pick ones that already have these values. And that means pick educated ones.
Keep the rest out. Period.
This is absurdly simple, and it's already the policy of nations such as Australia. In fact, it's even the policy of the allegedly "anti-immigrant" AfD political party, which explicitly endorses skilled immigration to Germany and explicitly cites (g, pdf, p. 59) "Australia and Canada" as models of successful immigration policy. Bet lots of you didn't know that!
For decades, Germany recklessly ignored education as a factor in immigration policy, pretending that all immigrants were equally capable of integrating into German society, and that a ridiculously easy "test" would solve all the problems. Germany is finally recognizing that limited immigration of educated people is the only sensible path, and ist starting gingerly down this road. It's decades too late, of course, and 2015's massive influx of uneducated immigrants remains a costly, destabilizing slow-motion catastrophe. But most German political parties have finally seen the light and committed to joining the rest of the developed world in preferring educated immigrants. The sooner change comes, the better.