Shemos 30:34-36:
The Lord said to Moses: Take for yourself spices, stacte, and onycha, and galbanum (ve-helbenah), spices and pure frankincense. They shall be of equal weight. Make it into incense, a blend blended by a blender, thoroughly blended, pure and holy. Pulverize some of it very finely and place it before the [Ark of] Testimony in the Tent of Meeting, where I will meet with you. It shall be holy of holies to you.Rashi quotes the famous midrash about why helbenah, a bad-smelling spice, is included in this mixture:
Scripture counts it among the spices of the incense to teach us not to look with contempt at including in our gatherings for fasts and prayers the sinners among the Israelites, that they should be counted (i.e., united) with us.This is frequently taken to imply that we must include the non-observant and/or heterodox in our communal activities. However, I believe this to be an incorrect interpretation.
The midrash (from Kerisos 6b) specifies that this is for praying and fasting. Rabbenu Bahya ben Asher, in his commentary to the Torah, explains that we must include sinners in our praying and fasting because they will repent and this will greatly enhance our communal prayer and fast. Rabbenu Bahya also cites the famous midrash about the four species we carry on Sukkos, with the aravah representing the sinner. Our use of the four species represents prayer (R. Joseph B. Soloveitchik addressed this issue at length), and we include sinners in our prayer for their repentance.
I do not think that this means that they must repent for every single sin they have committed. Even partial teshuvah is teshuvah. However, the inclusionary message of this midrash is only relevant to prayer and fasting in which teshuvah is a primary element. There is no indication that it applies to other undertakings as well.
As an aside, the Maharsha in his commentary to Kerisos states that this only applies to including a sinner to an existing minyan. However, he should not be counted for that minyan. I will leave this question for another time, but this is a matter of dispute with, I believe, the bulk of the posekim agreeing with the Maharsha.