If your mother is Jewish then you are Jewish according to halacha (the religious law). This means that your mother's soul must be Jewish and her body must be that of Israelite, so practising another religion by your mother excludes you being Jewish, according to halacha.
If it is your father is Jewish and not your mother, then you are still considered 'of Jewish descent' by the state of Israel. You are entitled to move and live in Israel if at least 1 of your grandfathers/grandmothers was orthodox Jew (that in practice means no convert) and you can enrol onto the hok hashvut (law of return). If, however, you want to practice in Jewish religious life you do need to convert as a gentile, but Reform Judaism (not seen genuine by real Judaism) recognises that person as a Jew also.
Again, you can see how ethnicity is an integral part of religion and vice verca, you cannot separate the two in Jewish identity as they are both its constituent members.
So the paradox is perhaps this that the more secular the Judaism the more emphasis there is on Jewish ethnicity, and the more religious/spiritual/mystical (Hasidism for example) the Judaism the less emphasis there is on ethnicity:
[video="youtube;0VNSKjpgPco"]https://www.youtube.com/watch?v=0VNSKjpgPco[/video]
0:43 Watch this Chabad Lubavitcher Rebbe Schneerson giving a blessing to the convert.