the official statistics of most European countries do show that foreign born people commit crimes at a higher rate than people born in that country.
Denmark publishes the stats in most detail but there’s plenty of other evidence from other western counties.
the US is slightly different as they have a much much higher crime rate than Western Europe generally and murders and rapes are much higher.
(possibly on that basis we should ban American migrants!)
so yes, this is true.
however the obvious response (don’t let anyone in from countries where the level of violence and/or misogyny is worse than Western Europe) means no immigration except from the EU (and even some of the EU countries are a bit suspect - the Balkan states have some not great records).
The U.K. cannot manage without immigration. We have a university sector that is funded from international students many of whom are not from Western Europe.
we desperately need carers and healthcare assistants and nurses and doctors and most of the migrants who come to fill those jobs come from societies that are more violent and more misogynistic than Western European ones.
as a country, we can just stop immigration. But there would be a massive, massive impact on our universities, our hospitals, our life generally.