I think both are valid and important to ask.
I think we do question British culture. That was what the discussion of rape culture and MeToo was about.
I think individuals have agency, and also that individuals are deeply shaped by the culture and circumstances they are brought up in.
I also think culture correlates with nationality fairly strongly (i.e. it's coherent and sensible to talk about the culture of a country, though it's inevitably a huge simplification).
Then the question then becomes an empirical one. We can and do survey men's attitude to women around the world. We do that because it's not a safe assumption that it's going to be the same everywhere. Why would it be?
It is certainly unjust to only ask cultural questions of non-white people. I think we should be open-minded to a full range of explanations on all things, and work out which ones explain the situation best.
If knife crime in Glasgow is linked to a specific toxic culture, I think we should talk about that, regardless of race. If there were a big problem in, say, the white protestant or white catholic community in Glasgow, I think it would be silly to say: can't consider that, it must just be socioeconomics.
Same with at least considering implications for immigration, which, to repeat, I am very much in favour of (and, just to put it beyond doubt, very much including non-white immigration).
I just don't think it's a moral failing to consider potential downsides as well as upsides of immigration, including cultural questions.
It was a moral failing at one point to question the church, or question men, or question all sorts of issues that were marked as taboo. I think that was wrong.