I think it would only be awkward if Harry and Ginny had broken up badly. In AUs where they break up amicably, I imagine that they’d still be close friends, and Ginny would be genuinely happy for her two friends. 

And in AUs where it’s a poly relationship between Harry, Luna and Ginny… well, so much the better.  

I imagine Mr Weasley would love talking to Luna about random stuff (he’s a very open-minded and kind man), and Mrs Weasley would be pleased to see Harry looking so happy. Bill would be baffled but pleased. Charlie would be discussing dragons with Luna and become her instant BFF. Percy wouldn’t know what to do except smile politely in mild bewilderment. Fred and George already knew Luna anyway, so they’d have no problems. 

Ron would be super supportive of Harry (and Ginny, if it’s a poly ship). He’d probably start by giving them both a massive hug, and then excitedly talking about them to anyone who’d listen. 

To answer your question, it would be cute rather than awkward. The Weasley are such a kind family, and they probably already half-knew Luna already due to her living so close. I don’t think they’d be bothered as long as Harry (and Ginny) were happy. 

Thanks for the ask, anon!

I love this, @queerqueenoftears! Thank you so much for sharing!