This isn’t really accurate.
I will address the latter part of your post first. Jewish law prohibits discrimination against covert Jews by born Jews and does not consider born Jews to be more Jewish than convert Jews.
For the first part of your post, one must remember that Judaism is an ethnicity as well as a religion (an ethno-religion), and so has cultural/religious rules regarding how Judaism is transmitted from one generation to another. It is my understanding that the transmission of Judaism is matrilineal, meaning that, as you said, one is a Jew if one’s mother is Jewish. However, some communities of Syrian Jews are stricter and would not consider someone a Jew unless both parents are Jewish, perhaps because of influence by the Druze, a fellow Mid-Eastern ethno-religious group which does not allow conversion and which generally practices strict endogamy.
Second, Judaism is not a proselytising religion and does not actively seek converts. Jewish rabbis reject a potential convert thrice before allowing him/her to begin the process of conversion, which is deliberately long and frustrating. This may give the impression of being exclusivist, but one would find it quite understandable considering that Judaism triples as an ethnicity, religion, and culture and that convert Jews are joining the Jewish ethnic group as well as the Jewish religion.
I may be misunderstanding your post, but I don’t see how this makes Jews elitist. I hope my explanation has cleared up any misconceptions on your part.
If I’ve misunderstood your meaning, I duly apologize.
I’m not Jewish, so allow me to tag @Pattylt so that she can look over my post in case I’ve made a mistake somewhere. Thanks, Patty!