Frankly that's arrogant and narrow-minded view; homogenous culture might cause less conflicts and problems when the culture itself is one promoting that in the first place
The countries with lowest crime numbers in EU per capita are (ordered by crime rate increasing): Slovakia, Hungary, Estonia, Cyprus, Slovenia, Czechia, Poland, Bulgaria, Croatia, Lithuania, Romania.
All of them are socially pretty homogenous. Most of them escaped Soviet block. Some even escaped Soviet Union. On the other hand, look at the countries from the other side of chart (this time, rate decreasing): Belgium, Spain, Portugal, Sweden, Luxembourg, Netherlands, Germany.
As this data concerns only EU, there is no UK here, but as I remember, it had around 3x crime rate as the Republic of Ireland, which would put it on the tops of the EU list.
Of course, increased diversity might not be the only differentiator between the countries from the top of the list and those from the bottom, but I think it defeats your point (almost as if you were racist for having irrational fears against living in a post-soviet society, which aren't backed by numbers).
The degree of ethnic homogeneity did not increase during that time, if anything it slightly decreased (or significantly in some major cities).
One possible explanation is that people willing to engage in low level crime simply moved to richer western countries because well they were (and still are) richer... e.g. in Norway Lithuanians are the second largest group of people who are imprisoned (after local Norwegians). The situation is similar in some other Western European countries. I'm not an expert but if I wanted to rob/steal from people and businesses I'd probably do that in Norway, Germany, or Switzerland rather than Romania or Lithuania. The risk versus reward ratio seems much better there. Also there prisons are way nicer (especially in Norway).
I would say, that based on my experience on growing in Poland (I was born in 1998), the people become richer and suddenly everybody now seems to be minding own business. So after you fill some economic needs, the will to pick on people decreases. But that will is surely dependent on how much you trust others are think similar (and won't rob you).
Anyway, the parents' commenter point was > near perfect "ethnical cohesion", doesn't stop crime or increase trust in any way
I can't see why should it be true. Perhaps it doesn't stop crime completely, but perhaps it actually increases trust. Based on the argument above we can't know.
The U.S. is one of the higher-trust societies, socially, while also being extremely racially diverse.
It sounds like pro-social culture and your people being rich probably matter more than race, and Eastern Europe has a critical deficit in both of those. :p
Then again crime rates in Belarus for instance don't seem to be much higher than in Poland or Lithuania.