As usual, there are many answers to this question, all of them are related.
First, let's start with a brief history. In the time of Abraham, Abraham did try to convert many people. He did this by having an open tent which allowed people from every direction to come and learn about Gd. Then, in the time of the Exodus from Egypt, the Jewish people again, accepted any converts who would come to the Jewish people and become part of the nation. In Jewish tradition these people were referred to as the "Eruv Rav" or the "Mixed multitudes of people" who did not come from the Israeli tribes, but who saw the miracles that happened in Egypt and wanted to attach themselves to Gd.
Traditionally, the Eruv Rav was the source of many bad things that the Jewish people did. Some explain, that this happened because while they were awed and inspired by Gd, they were not truly loyal to the Jewish people.
Jump forward a few hundred years, and before the time of Christianity, the leaders of the Jewish state, were fighting a war with the Idumeans. After winning the war, and being tired of the constant fighting over generations, the leaders decided to convince the Idumeans to all convert to Judaism. They did so, and centuries later, some Jews of Idumean decent (namely King Herod) attached themselves to Rome, became leaders of Israel and were very cruel to the Jewish people. Again, their loyalty to the Jewish people was questioned.
So Jews in general, do not like mass conversions of people who are joining the "winning team". There is a question of their loyalty to Judaism and the Jewish people. In other religions like Christianity and Islam, this is not such a big deal, because those are religions made up of many nations, while Judaism is a religion only made up of a single nation. You can't be Jewish and not be part of the Jewish People.
On another level, we are not concerned about losing many members, or not having enough Jews around. In the Torah, Gd says not to count the Jewish people directly, or else a plague will come about. We are also promised that we will be an eternal nation. We will never die out. Because of this promise, and a general statement that our numbers should not really be counted (except when absolutely needed, like to build community projects or help the poor) there is no concern that we are "too small", or that other groups of people are larger than us.
From the perspective of Judaism, we know what is correct and right for our people. We know the Truth, and we are not in competition with anybody else in the world. We share what we know about Gd and his unity, and about living in a Just society. The rest of the details of how other nations live is not our concern. As long as people act Justly and Peacefully and don't try to take away our home from us, we let other people live however they wish to live.