Sweden, from Wikipedia:
According to
Eurostat, in 2010, there were 1.33 million foreign-born residents in Sweden, corresponding to 14.3% of the total population. Of these, 859,000 (64.3%) were born outside the
EU and 477,000 (35.7%) were born in another EU Member State.
[22][23]
So roughly 64% of foreign-born people are not from the EU. We don't have data on racial make-up considering second and generation immigrants, but we do have this statistic:
As of 2017,
Statistics Sweden reported that around 2,439,007 or 24.1% of the inhabitants of Sweden were from a foreign background: that is, each such person either had been born abroad or had been born in Sweden to two parents who themselves had both been born abroad.
[20] Also taking into account people with only one parent born abroad, this number increases to almost a third in 2017.
[21]
So 64% of foreign-born people are not from the EU. Not all of those are non-white by American standards, so let's say 50% of foreign-born people are non-white. I would say that that is a fair assumption seeing as we don't really have that much immigration from non-EU majority white countries, as shown by this data:
By American standards, being mixed race would count you as non-white as well. So 1/3 of the population has one parent who was not born in Sweden, and roughly half of those non-Swedis parent would then be non-white. So we can estimate the number of non-white people to be around 16% of the population. Yes, I know that this is not perfect maths before a pedant chimes in to say just that, but it's probably the best estimate we can get with the numbers available, since Sweden doesn't really track race. (And the reason why countries like Sweden and Germany doesn't track race is NOT as OP suggests because we're all racists, but because the discussion about race is very different in Europe, because in countries like Sweden and Germany we had racists dividing people into races and discriminating based on that and measuring brain size and that kind of thing and during the second half of the last century we realized that that was hugely problematic, and so we stopped tracking race on the government level, because of how doing so and race "science" that had been used to carry out and justify Nazi atrocities.)
So how does that correlate with the demographics of parliament? 43.6% of members of parliament are female, so that does not quite reflect the general population. Only 8.3% of members of parliament were born outside the country which is quite a bit lower than the 14.3% of the entire population.