Where the work happens
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Most soap is made in a home, and the space question splits into two: what the process needs and what the rules allow.
A kitchen, usually
Water, a flat heat-tolerant surface, ventilation and power. That is genuinely the requirement.
Which is why this craft starts at home more often than any other in the estate.
And why the constraint that appears is space for the cure rather than space for the making.
What the space has to give you
Ventilation at the lye-mixing step.
A surface that a caustic splash will not ruin, and a floor you can wash.
Somewhere to put a hot container down that is not near anything else.
And a way to exclude people and animals for the duration, which is the control that prevents the accident rather than treating it.
Separating it
Dedicated equipment: the stick blender, bowls, spatulas and molds are soap equipment and not kitchen equipment again afterwards.
Dedicated storage for lye, sealed and labeled and out of reach.
And ideally dedicated time, so food is not being prepared on the same surface the same afternoon.
This is worth doing even where no rule demands it, because it is the difference between a hobby and a manufacturing process.
Where it stops being a kitchen
Volume is what changes the question: a quantity of sodium hydroxide stored in a residence can reach local fire and building rules, and a home business can reach zoning.
Cottage food exemptions generally do not help, because they cover food.
And the cure racks usually force the move before the regulations do: at a few loaves a week, a spare room is already committed.