I am of the Less is More, school of tack cleaning.
Once a season (winter, spring, summer, fall) I bring my tack home, take everything apart, and clean and oil it. I use Higher Standards soap (or castille) and then Neats Foot Oil–the pure stuff, not the compound. Occasionally, I will bring something home “out of rotation” and clean it and use either the HS balm or Effax instead of the oil (I actually don’t like how either smells, TBH). Occasionally, I will also wipe down tack at the barn with a wet microfiber cloth. Especially my mare’s flash, as she has a dirty mouth and it’s often gross after a ride.
The exceptions are my hunt tack, which gets cleaned weekly during formal season and then treated with Effax (or the HS balm). If the tack gets soaked from rain, I will oil it instead.
My schooling saddle and bridle are both 15+ years old and have lived their lives like this–they’re in great shape. My hunt saddle is younger, and the bridle is younger still, but are also looking and feeling good.
I have never had problems with mold until this past summer when a fellow boarder let her tack develop a nice, thick patina of it and the whole tackroom suffered. I’ve also never had a problem with rot from the oil. I DID have a saddle that had a split under the gullet once because I overdid it with the glycerine soap and though it looked pretty, it was sealed like a drum and no moisture ever got through to the innards of the leather.