Proper vetting is an essential first step, yet both the head of the FBI and Homeland Security have said this is not possible with people coming from certain parts of the world, including Syria, for example.
A great many of the migrants entering Europe over the last couple of years were not vetted, had no papers, or had several sets of forged papers, and they were allowed in anyway, even though Isis admitted to using the migrant crisis to flood Europe with thousands of operatives. So we'll see how that turns out.
Another issue is that multiculturalism provides an environment in which fundamentalism can flourish unchecked and hidden from view. This approach to immigration seems to simply encourage a lack of integration and to produce divided societies where the intolerant beliefs you mention can be reinforced by likeminded people and not be as exposed to challenge as they should be.
In the UK 23% of Muslim women speak little or no English, a complete barrier to integration, and a quarter of Muslims want some parts of the U.K. to be governed by sharia law. Over half think homosexuality should be illegal in the UK. Living in a society within a society means that such views are not successfully challenged. Add to this the fact that they can watch non stop Arabic / overseas tv / internet channels, send their kids to islamic schools, have separate Islamic centres for socialising etc etc, and it's easy to see how integration, and exposure to more tolerant views as the norm, can be kept to a minimum, if desired, and even if it isn't particularly.
And no doubt this approach provides a great environment for the Isis terrorists we've welcomed into Europe to remain under the radar, and also fosters the 'them and us' attitude that plays a role in yet more radicalisation of the young. The recent ICM poll also found that 66% of UK Muslims would not inform the authorities if someone close to them had become involved with terrorist sympathisers, ie those likely at the beginning of the process of their radicalisation.
Also, the vast majority of people entering Europe during the migrant crisis have been fighting age angry males. Under the auspices of multiculturalism, these young men will inevitably find themselves in areas where there are high concentrations of Muslims, many of whom are not well integrated in the first place. Not very sensible, IMHO.
Multiculturalism, IMHO, has led to the development of what Trevor Phillips (commenting on the recent ICM poll on UK Muslims) calls a "‘chasm’ and that this has developed "between the attitudes of many British Muslims and their compatriots, driven by their adherence to their faith."
What to do? IDK. Phillips has outlined a strategy he thinks would be successful, I'll post more on that later, assuming the thread remains civil

but basically it seems to consist of dismantling the infrastructure of multiculturalism to some degree (for which the champion of the term islamophobia in the UK has been vilified - as an islamophobe - of course. Oh the irony

).
ICM Unlimited | ICM Muslims survey for Channel 4