Why is it so important to convince non-observant Jews to keep the mitzvot?
There is no greater love than a loving endeavor to save one's brother from distress
Concerning the generation that witnessed the destruction of the First Holy Temple, our Sages teach that if they had held the Torah in esteem, the light within it would have restored them to the good path, and the Holy Temple would not have been destroyed. The Sages teach elsewhere that the Second Holy Temple was destroyed because of undeserved hatred.
We are living in the generation which can hear the approaching footsteps of Moshiach, a stage by which "all the propitious final times for the coming of the Redemption have already passed, and the matter now depends only on repentance and the performance of good deeds." At a time like this, particular effort should be invested in these two areas: ahavas Yisrael, loving a fellow Jew, and endearing the Torah and its mitzvos to the hearts of our brethren.
Both of these goals are attained simultaneously when we teach our brethren to follow the Torah, for there is no greater love than a loving endeavor to save one's brother from the distress that would result from his misdeeds. Furthermore, how can one make the Torah more esteemed and more cherished than when one explains to one's fellow Jews that the Torah is G-d's will and wisdom, that it remains eternal at all times and in places, and that through it G-d has implanted within us the life of the World to Come!
From a letter of the Lubavitcher Rebbe, in Likutei Sichos, Vol. XIII, p. 291. Excerpt: From Exile to Redemption