Shavuot is the festival most relevent to converts to Judaism, as the Book of Ruth indicates. She is the most famous convert, and indeed is the ancestor of King David and, by extension, the Messiah. In truth, all Jews "converted" on Shavuot by accepting the Torah.
So many religions proselytize, and actively seek out converts. Some do it at the edge of the sword. What does Judaism think?
Easy. We love converts, and do not encourage them to do so. A convert is very holy, having freely decided to accept 613 commandments. They did not have to in order to gain entry to The World To Come. Any human being living in accordance with the rules of morality finds great favor in God's eyes. This spiritual person could have become a "Noachide", an observer of the Seven Laws of the Sons of Noah. Yet they chose full-blown Judaism. Inspiring.
In the quality versus qualntity argument, Judaism chooses quality. Once in history did Jews actually force the conversion of a people. Back in the days of John Hyrcanus, more than 2000 years ago, Judea offered the Edomites the choice of conversion or exile. Many chose exile, and many chose conversion. Among the descendants of those converts was Herod, the monumental - and bloody - king of Judea.
Was it the right thing to do? Who knows. On the one hand, Hyrcanus immediately neutralized the security threat posed by the Edomite enclaves in Judea's side. Maybe Israel should offer the same deal to the Palestinians! And in the long term, most of those conversions seem to have stuck.
On the other hand, it is an affront to Judaism's belief in the value of all nations to force conversion. We do not regard "Lions converts", ie, converts from fear or coercion, highly.
That really is the bottom line, but not to be taken to the extreme. Some wish to eliminate conversion altogether, and others restrict it where it is really needed.
I believe that in cases of some Jewish lineage, or doubtful lineage, conversion should be ACTIVELY encouraged. In cases where the conversion is for marriage, it should not be encouraged. If the marriage is already in place, then it can be encouraged.
Why? Because conversion for marriage is often insincere. It is done to alleviate the guilt of the families. If, however, the couple is already married, the reason for the conversion is no longer to please the families, but to reconcile the home. That is more sincere, and I belive the rabbis should examine these cases with a favorable inclination.
We need not fear conversion. In many situations today, a new, welcoming approach is called for.
But there is one type of proselytizing we MUST do. We must encourage ALL humans to live by the 7 Noahide laws of basic morality. That may be done even by force. After all, the purpose of the Jewish people in the world is "to fix the world under God's Kingdom."