as women doesn't wear altar clothes (especially nuns) in your country, we don't wear veils in our country too. I think it makes some sense about how much religious we are. If you ask a Turkish, what's your religion ? he/she says Muslim but you can't see him/her when she/he prays or in mosque (mosques are nearly-empty), or wearing islamic dress.
You are talking like going to mosques is a wrong thing. Why does Islam disturb you? I think you don't see the reality in Turkey. There are so many girls, woman wearing head scarf. This is very normal because at least %90 of the population are Muslim and head scarf is a reality of Islam. And there are so many girls wearing mini skirts and bikinis on sea side although they are Muslim or not. That's a personal choice. I love the mix in Turkey.
I can understand you, you think Turkey has a wrong image abroad and you want to show the real Turkey but people can see the truths if they want because today technology, internet made everything clear.
Yes, Inna looks Arabic more than Turkish in that picture but you know, there are some similarities between Arabic and Turkish culture so people can be confused. You shouldn't be disturbed so much because of this. Everybody knows we are not Arabs but we are Muslim like Arabs.