I've solved it.
I just used a subselect. Worked very quickly. I had a lot of trouble with
subqueries when I first started databases with MySQL. So I have been afraid
of them.
update entities
set customer_status = select(customer_status from entity_dimension_update
where entities.entity_id = entity_dimension_update.entity_id);
Worked almost instantly.
My apologies for the spam.
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matthew(dot)pugsley(at)gmail(dot)com