Acceptable seems a strange choice of word to me. People wear all sorts of stuff that I don't like and personally would never wear. But I wouldn't call their clothing choices unacceptable!
Personally I love double denim. What else is a denim jacket for? If I'm wearing shorts or linen trousers it's probably too hot for a denim jacket. I 'd also wear one with chinos or cargo trousers I suppose. What sort of jacket do people wear with jeans otherwise when it's too warm for a 'proper' coat?
And if it's good enough for Lydia Tomlinson, it's definitely good enough for me. I think she is incredibly stylish!