Is it rude to make enquiries about the lives of others?

It's not rude but there is an etiquette to be followed. The enquiry must be substantiated with proper reasoning as to why one needs to know. Open ended blunt question is rude as it perplexes the other.

Once a man his wife works in a bank and I asked whether she is retail or corporate banking.. the guy was surprised and said I was the first to ask so decently as others directly ask "Is she a cashier ?"

From my experience British people find all questions impolite