Im a British Indian girl and personally I would prefer to date a western born indian boy (im dating an australian indian boy). My family feels the same way but they wouldn't staunchly oppose a marriage to a guy of another race as long as he possessed good values (& isnt muslim lol). So we Indians tend to be family orientated, have great respect for our elders, strive to be successful and work respectable jobs and be relatively cultured. We are not a closed off group and Indians are quite open minded. My male cousin has a white girlfriend and although my grandma doesnt like it and his parents would prefer he date an indian girl, they are supportive of him and even invited his girlfriend and her family over for Christmas.
The reason why i personally prefer to date an Indian guy is because he understands my culture, we can pass it on to our children, im quite a political person too so our allegiences would be more likely to tie in together, i have a dual identity of british/western born and indian and hed share that, he wouldn't force me for sex before marriage, hed understand that his family has to approach mine to marry me and we have a shared religion, hinduism, of which i wish to learn more about.
If youre looking to date an indian girl and be accepted by her family, in particular, you need to have an understanding of our mildly- moderately conservative culture. Which you will learn from her in time. But theres not much to it really. Just respect her parents and assure her family that the kids will have a sense of their indian culture and x religion as well as yours. Indian parents are most worried about that if anything.