In theory they are independant but in order to advance tiers 1-4 are gated by quests between proficiancy (first xp bar) and mastery (2nd xp bar). Depending on the craft it might be in a higher level zone where you will need protection or help to do it.
Farming, Forestry and Prospecting are NOT gated by quests. To collect materials you would need to go in higher level zones, but you do not need to collect. My level 50 jeweler (at the time) got to Master Supreme without setting foot in Moria or even Eregion (where much of the high-level materials are).