Firstly, this is nothing to do with Customs. Customs is about what you have in your baggage. We're talking about immigration here. Which might be called passport control. You go through immigration/passport control first, then you collect baggage at baggage reclaim, THEN you go through Customs because that's all about baggage.
Yes, you have to join the line that matches your passport. If that splits you from your family, then hard luck, you have to go through in different lines. They might make exceptions for minor children so they stay with their parents, but apart from that, you have to go separately.
This is only likely to affect you coming home. Visit a country where none of you are citizens, and you're all foreigners according to them so you all go through together.
And what's a foreigner? In the USA, yes, it's one set of lines for US citizens and another one for everyone else. But I'm British and we're part of the European Union (for now!) and that's all one country for passport purposes. So what you get in an EU country is the EU line and the "other" line. When I travel with my German friend, we can go together in the EU line. When the UK has left the EU, that will probably change.