I am an IT graduate with good evaluation and a good job and - by god's will - a good future Inshaa Allaah. I come from a reserved family, my parents are religious, my mother teaches and studies Fiqh and Sunnah and Tafseer and other Islamic topics, me and my brothers do the prayers 5/5, at mosque my father and sister know the Holy Quran by heart.
I was graduated recently, and I admired a girl there never talked to her, never said anything to anyone about the subject. Just admiring her from a distance, even she has no clue. I am not into girls and I don't speak or deal with them except formally and for necessities only. I need to know if it would be wrong to propose for such a girl that comes from a totally different background (talks to guys, hangs out, wears inappropriate clothes like jeans and shirts as lots of the girls these days), I asked about her some says she is a very nice persons others say she is low in morals because she hangs out with guys and had a boyfriend once. But she is a nice person in her inner self and I know it, for that I observed her and her friends and colleagues and how she deals with them and draws her own lines. I do believe that it is not her fault that she is opened to guys and relationships but her parents', and if she was raised as I was she might make a better person than myself, and I do believe that maybe with the right guidance she might get back on the right track and make a good and loyal wife and a mother in the future. I know that even mentioning this kind of topic with my family will cause serious problems and arguments like: she is different, she is no good for you, how do you expect us to live with a person like that, over my dead body. I am asking for advice here not for a Fatwa and what do you think I should do to accomplish what you suggest for me as an advice.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

We do advise you not to think about this girl for many reasons:

1) She is not religious as you mentioned.

2) Who knows whether or not she will change her attitude and adhere to the rulings of Islam?

3) You are obliged to please your parents and respect their opinion for the great rights they have upon you.

If you leave something for the sake of Allaah, the Glorified and the Exalted, He will grant you better than what you left.  For details read Fatwa: 88338.

Allaah Knows best.