Can I take my compost to a composting site on Shabbat, within an Eruv? Is there a Muktzah issue? An uvda d’chol or tircha issue? I wouldn’t want to shlep a bag of trash ten blocks on shabbos, but composting is fun and almost feels, I don’t know, like I’m contributing back to the earth. I don’t have a weekday when I’m walking in that direction, and dropping it off before Shul makes sense for me.
The first issue to consider is that of muktzeh. The compost has no function and is also disgusting. It should therefore, presumably, be defined as muktzeh and assur to move. The matter is not so simple, though.
The Gemara (Beitza 36b) tells us that we are permitted to remove a used bedpan from the house and place it on the garbage heap. The Gemara in Shabbat (121a) discusses this as well. In both of these sources, it is clear that excrement is not the only thing that can be removed; both mention a dead mouse as another example of the same principle. The Rambam (Hilkhot Shabbat 26:13) and the Shulchan Aruch (O”H 308:34) rule according to this position. Rav Moshe Feinstein (Iggrot Moshe O.H. 5:21:2) notes that the definition of repellant is subjective; what is repellant for one person may not be so for another. It would appear that compost could be one of these repellant things. If it is an eye-sore for you or it stinks and you cannot stand the smell, (Mishna Berurah 108:131), you may remove it from the house on Shabbat.
There is another reason to permit moving the compost, beyond simply the analogy with the bedpan. The Shulchan Aruch (following Tosafot (Shabbat 143a s.v. Atzamot)) rules that one can remove bones and peels that are appropriate for animal feed from the table (S.A. 108:27. See also S.A. 108:29 and M.B. ad loc 119). Spoiled food in a kitchen compost container is certainly appropriate to feed dogs (not that anyone would) and should be permitted to move.
The question remains, however: can you take it to the composting site on your way to Shul? Or, should you perhaps dispose of it in the quickest way possible? The Tosafot (Beitzah 3b) rule that if one picks up an object that is customarily used for forbidden labor on Shabbat or because they need the space where it is resting), one does not have to get rid of it as soon as possible, rather, one can place it wherever seems most convenient. This is ruled in the Shulchan Aruch (108:3 see Magen Avraham 108:7 and M.B. 18:13). This should apply equally to a compost bin, even if one assumes the more stringent ruling, that it is permitted because it is repellant.
All this being said, I am still not sure that it is appropriate for you to dispose of your compost on Shabbat. As far as your personal practice is concerned, there would appear to be no concern of uvdin de-chol, acts that are not appropriate for Shabbat. You have stated that you never walk in that direction except to attend Shul on Shabbat and that the act itself has a genuine religious meaning for you that is particularly appropriate for Shabbat. I am more concerned with the communal norms. Shabbat, in addition to other things, is also about communal culture. You can best gauge how your community will react to this practice. If you feel it will lead to conflict, I would urge you to simply do it on another day.
I want to be clear about one more point. It is absolutely forbidden from the Torah to spread your compost, fully decomposed or otherwise over living plants in a garden or field. Taking your compost to a composting site should avoid this problem but be sure not to dispose of it in any way that resembles spreading it on the ground.
N.B. My teacher and mentor Rabbi Dov Linzer has commented that other similar cases would raise uvdin de-cholconcerns. In general, it would clearly be an uvdin de-chol issue to reserve one’s chores for Shabbat. For example, one should not wait till Shabbat to bring bags of garbage to the dump because it is a more convenient time to do so (or because it happens to be on his way to shul). Composting however might be quite consistent with the spirit of Shabbat. Rather than the making use of the world, composting is a way of withdrawing from the artificial manipulation of the world, and repairing it to a certain extent. Not only is this act objectively consistent with the spirit of Shabbat, it is also experienced as such by you subjectively. Your subjective experience is a significant factor in the parameters of uvdin di’chol (see S.A. 302:1). For you, certainly, this is not an uvdin de-chol concern, and may be done on Shabbat assuming that it is appropriate for your community.